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\^*i:- ^ a>° -vMa>c- 






MANUAL 



OF 



Elementary Logic 



DESIGNED ESPECIALLY FOR THE USE OF TEACHERS 
AND LEARNERS. 






BY 

LYMAN H. ^TWATER, D. D., LL.D., (?{V^ CL^l 

PROFESSOR OF LOGIC AND MORAL AND POLITICAL SCIENCE EN THE 
COLLEGE OF NEW JERSEY. 



REVISED EDITION. 



PHILADELPHIA: 

J. B. LIPPINCOTT COMPANY. 



\ 



\ 



>c 



.h 



a 



s 



Entered according to the Act of Congress, in the year 18G7, by 

J. B. LIPPINCOTT & CO., 

In the Clerk's Office of the District Court for the Eastern District of 
Pennsylvania. 



Copyright, 1895, by Addison Atwater. 



CONTENTS. 



PAfll 

Prei ice • 9 



CHAPTER I. 

THE SPHERE AND OBJECTS OF LOGIC. 

Section I. Logic the Science of the Laws of Thought 13 

IL The General Nature of Logical Judgments. 22 

III. Reasoning as including Conceptions and Judg- 

ments 25 

IV. Pure and Applied Logic • 23 

V. Applied Logic further explained 34 

VI. Utility of Logical Study 36 

VII. Fundamental Axioms of Logic •••••••••• 40 

CHAPTER IL 

CONCEPTIONS. 

Section I. Conceptions, their Nature and Formation............ 43 

II. Higher and Lower Conceptions 47 

III. Genus, Species, Essence, Differentia, etc 49 

5 



g CONTENTS. 

PAQl 

Sect. IV. Other Distinctions in Genus and Species 61 

V. The Three Powers of Conceptions 63 

VI. Inverse Ratio of Extension and Intension 66 

VII. Denomination of Conceptions 56 

VIII. Various kinds of Terms 68 

IX. Quality of Conceptions 64 

X. Notative and Symbolical Conceptions 67 

XI. Logical Division 69 

XII. Definition 73 



CHAPTER III. 

JUDGMENT. 

Section L The Constituent Parts of a Judgment 82 

II. Quantity, Quality, Relation, and Modality of 

Judgments 87 

III. Quantity of Judgments 87 

IV. Quality of Judgments 89 

V. Distribution of Terms in Judgments 91 

VI. Relation of Judgments 91 

VII. Substitutive Judgments 95 

VIII. Analytic and Synthetic Judgments 100 

IX. Modality of Judgments 101 

X. Plurative Judgments 102 

XL Conversion of Hypothetical into Categoricals 102 



CONTENTS. 7 

CHAPTER IV. 

REASONING IMMEDIATE INFERENCE. 

PAG1 

Section I. Mediate and Immediate Inference Denned «. 106 

II. Immediate Inference by Opposition 107 

III. Immediate Inference by Conversion 113 

IV. Other Modes of Immediate Inference 117 

CHAPTER V. 

REASONING MEDIATE INFERENCE. 

Section I. Introductory Observations 123 

II. Moods of the Syllogism 132 

III. Its Four Figures 133 

IV. Aristotle's Dictum and other Maxims 138 

V. Unfigured Syllogisms 142 

VI. Hypothetical Syllogisms 144 

VII. Conditional Syllogisms 145 

VIII. Disjunctive Syllogisms 146 

IX. The Dilemma 148 

X. Incomplete Syllogisms 152 

XI. Complex Syllogisms 153 

CHAPTER VI. 

APPLIED LOGIC — FALLACIES. 

Biction I. Fallacies, Formal and Material 158 

II. Fallacies, partly Formal and partly Material 166 

III. Logical Puzzles 179 



g CONTENTS. 

CHAPTER VII. 

APPLIED LOGIC — METHOD. 

PA<31 

Section I. Original and Derivative Sources of Knowledge.... 186 
II. Problematic, Assertory, and Apodictic Judgments, 193 

III. Deductive Reasoning 196 

IV. Inductive Reasoning 197 

V. Hypothesis 207 

VI. Analogy 211 

VII. Categories 213 

VIII. Harmony and Co-ordination of the Sciences 217 



APPENDIX. 

APPENDIX A. 
examples for logical praxis. 223 

APPENDIX B. 

SYSTEMS OP SYLLOGISTIC NOTATION. 

Notation by Circles • 248 

Notation by Straight Lines 250 

The Hamiltonian Notation ........ 252 



PREFACE. 



The object of this volume is to furnish a text-book of in- 
struction for the use of teachers and students of Elementary 
Logic. This object has determined its contents and form. 
It does not claim to offer any new contribution to the 
science of Logic, as such, although it is quite possible that, 
in some instances, the author's way of illustrating known 
truths may have shed some new light upon them. Still 
less is it designed to present an exhaustive treatise contain- 
ing all the truths pertaining to Logic which have beeD 
reached by the great masters and expounders of the science. 

But, as before stated, the object is to present the great 
elements of the science in a form suited to the wants of 
teacher and learner. Books for this purpose of decided 
merit are indeed now in use. Many of them, however, are 
not constructed in conformity to the now recognized con- 
ception of Logic, as the Science of the Laws of Thought. 
Others are too extended, cumbrous, or abstruse, for ele- 
mentary instruction, especially within any time that can 
possibly be allotted to this study in our Colleges and High- 
schools. Some of them need much previous drill in more 
elementary treatises as a propaedeutic. 



10 PREFACE. 

At all events, the author in this brief manual has at- 
tempted to meet a want which has become urgent in his 
own personal experience as a teacher. How far it meets 
the wants of others remains to be seen. He can only be- 
speak for it a candid judgment and fair trial. 

It is only just to add that he has freely used whatever 
best served his purpose in the works of other authors, some- 
times without explicit mention of the sources from which 
he has drawn. It is proper, however, to say that he is in 
greater or less degrees indebted to the works of Whateley, 
Kant, Hamilton, Mansel, Bayne, De Morgan, Wilson, 
Bowen — and most of all to Thomson's Laws of Thought. 
He trusts this general acknowledgment will suffice for all 
cases in which none more specific is made. 

Perhaps no better place will occur for stating, that occa- 
sional paragraphs will occur of such a description that, 
though important, they may be postponed for review, or 
omitted entirely, if pressure for time requires. It is of 
course always the teacher's province to judge how far any 
portions of the several chapters may be wisely postponed 
until the time of review. The author will, however, sug- 
gest that Sections IV. and V., of Chapter I., may advan- 
tageously be deferred until the student reaches Chapter VI. , 
when it will form a suitable introduction to the study of 
applied Logic. The beginner can better understand and 
appreciate it at this point, than in that natural order in 
which it is treated in defining the sphere and objects of 
logical science. The same view applies in a less degree to 
Section VII. of the same chapter, on the Uses of Logic 



PREFACE. 11 

Portions of this will of course be better understood after 
the student has learned somewhat of the principles involved. 
On the other hand, it is a strong reason for giving early 
attention to it, that some idea of the advantages of the 
study is a strong stimulus to the student to make the effort 
necessary for its successful prosecution. 



NOTE TO EEVISED EDITION. 

While such minute corrections of the main text of 
this treatise as have been found needful will be found 
in this edition of it, the chief improvement consists 
in the large addition of examples for logical praxis 
which so greatly facilitate the teaching and study ol 
Logic. 

Princeton College, 1879. 



ELEMENTARY LOGIC. 



CHAPTEE I. 

THE SPHERE AND 0BJECT3 OF LOGIC. 

SECTION I. 

1. Logic is the science of the law3 of _ , _ _ 

Logic defined! 

THOUGHT OR THINKING. 

2. Of these two words, thought and thinking / 
we shall hereafter use the former to denote the 
object matter of Logic. Thought may Thinking or 
denote either the process or the product . °^. g ** ^ , 

r r jective and od- 

of thinking, i. e., it may be taken either jective. 

in a subjective or objective sense. Logic is the 

science of the laws of thought in both senses; the 

laws which govern genuine thinking itself, and 

also the relations of the products of thought to 

each other, and to all matters to which they are 

applicable. 

3. Object means that about which the mind 
thinks; Subject, the mind itself. The Snbject and Ob- 
adjectives subjective and objective, and the Ject e 

2 13 



14 LOGIC. [Chap. I. 

adverbs subjectively and objectively, have a corre- 
sponding import; the former in each case referring to 
the mind considered as the subject of conscious states 
of knowing, thinking, feeling, willing; the latter 
referring to whatever becomes an object of the 
niind's attention. And since the mind may make 
itself, its own states and exercises, objects of its 
attention, it is said, in this case to objectize itself, or 
become a subject-object When it is 
needful to discriminate other objects 
from this subject-object, some writers use the term 
object-object. The student who under- 
stands the foregoing, will easily under- 
stand the terms objectively and subjectively, when they 
come in his way. The sooner these terms are under- 
stood, the better, as they are of constant occurrence, 
not only in philosophy, but in general literature. 

4. The next step in clearing the subject is to 
Thought de- determine what thought is. 

working and Thought is subjectively the operation, 

product of the an( j objectively the product of the Dis- 
Discursive Fac- 
ulties, cursive Faculties of the mind. 

5. It becomes necessary now, in order to make 
this definition complete and intelligible, to explain 
what we mean by the Discursive Faculties. A] though 



Sec. L] ITS SPHERE AND OBJECTS. 15 

this is properly within the province of Psychology, 
yet it is at one of those points of con- Tne discursive 

_ Faculties ex- 

tact between it and Logic, which re- plained. 
quires to be explained in defining the object-matter 
of either. 

6. For our present purpose then, the faculties of 

intelligence, (leaving out of view me- Twofold divi- 
sion of Intellec- 
niory which retains and reproduces tual Powers. 

what is given by the other faculties), may be di- 
vided into two great classes — the Intuitive and the 
Discursive. 

7. The Intuitive Faculties are those which dis- 
cern objects, phenomena, or presentations immedi- 
ately, and not indirectly, i. e., not Intuitive Fac . 
through the medium of any process of ^ties described. 
thinking. Thus, the objects perceived by the 
senses are known intuitively, as whatever we see, 
hear, touch, taste, or smell. So also our states of 
consciousness, our feelings, volitions, cognitions, at 
the moment of their occurrence, are known intui- 
tively. The mind knows them immediately, intue* 
tur, by a direct beholding, and without the inter- 
vention of reasoning or thinking. 

8 The Intuitive Faculties furnish us T ^Wsh 

the material of 

the original material of all our know- Thought. 



16 LOGIC. |Chap. L 

ledge. xhe Discursive Faculties take the matter 
The Discursive thus furnished, and proceed from it, 

elaborate it in- 
to new forms, discurrunt, to new results founded upon 

it. They work it up or elaborate it into new forms ; 
Why called Ela- hence by Hamilton and others, they are 
borative. called the Elaborative Faculties. 

9. It is important to observe, that intuitions 
Intuitions are (aside of exceptions in the region of 

of individual ob- 

jects. self-evident supersensual truths), that is 

to say, intuitions of material things or of states of 
consciousness, are always of individual objects, 
never of classes of objects. By the senses we per- 
ceive individual trees, stones, or animals. But the 
Further Intel- senses do not apprehend them in classes. 
lectuaipro- rp c i ass ify [ s ^o perform a process of 

cesses are dis- J r r 

cursive. Abstraction and Generalization, i. e. of 

Thought, and goes beyond intuition. So of states 
or acts of consciousness. They are first perceived 
singly, not in classes. Now this pure intuition is 
Logic concerns not thought strictly so-called, nor in 
the former! the sense here intended. It furnishes 
matter for thought, but is not thought. With 
this logic does not concern itself, unless casualty 
and indirectly. It develops the laws of the think- 



Bee. I. ] ITS SPHERE AND OBJECTS. 17 

ing process, and of its products, in their constituent 

parts, combinations, and relations. 

10. The Discursive Faculties are those which 

take the materials furnished by intui- Discursive 

tion, and, by a process of thought, in- Fac d ^ es / n r °* 

volving Analysis and Synthesis, reach l J s[s t and Syu- 

'" to new 



now results. First, they separate or results. 
analyze the single objects or wholes given in intui- 
tion into parts. They notice one or more of the 
parts into which any individual whole is thus 
analyzed, to the exclusion of the residue. That is, 
they abstract them from the rest. Thus, suppose 
that this book be the object beheld. It has exten- 
sion, figure, solidity, color, is composed Abstractioil ae . 
of printed sheets, enclosed in binding, scri bed. 
and is a treatise on Logic, etc. Xow the mind may 
attend to one or some of these properties, neglecting 
the rest. This is Abstraction. 

11. Again, the mind, observing a number of ob- 
jects that agree in one or more particulars singled 

OUt by abstraction, forms a class Or Generalization 

illustrated and 
genus of objects which so agree. Thus, explained. 

noting extension, not only in this book, but in every 

material object, it classifies them as extended ob- 

: }cts. Observing that, besides extension, they have 

2 * ■ B 



18 LOGIC. [Chap. 1. 

solidity, it forms them into the genus, bodies or 
matter. Noting also that many of these agree in 
being composed of sheets of paper for the purpose 
of containing written or printed language, it classi- 
fies them as such, under the name of books. This 
s the manner in which it forms genera or classes 
from individual objects. And to do this is to gene- 
ralize. It is obvious, moreover, that generalization 
may proceed, not only from individuals to classes, 
but from lower genera to higher, which comprehend 
them : as from white-oak, yellow-oak, scrub-oak, 
live-oak, to oak; and from oak, hickory, ash, etc., 
to "tree ; and from tree, grass, flower, grain, etc., to 
vegetable ; and so on, till we arrive at the highest 
possible generalization (summum genus), wdiich is* 
Being. Hence Logic treats first, 

OF CONCEPTIONS.* 

12. The product of this Generalization is con- 
ception (con capio) the taking of many together in 

* This is the meaning to which logicians now limit the word 
conception, viz., that act or 'product of the mind which is denoted 
by a general term, and is obtained by generalization. In common 
Bpeech, it has a much broader import, ard is used almost sypony- 
mously with that loosest of words, idea, i. e. for almost any men- 
tal act or representation. And by philosophers it has beep used 



Sec. I.] ITS SPHERE AND OBJECTS. 19 

one, i. e. in one class, denoted by one name. This 
conception or the name denoting it, re- 0oiice . ex- 
presents, not all of any individual ob- P lained « 
ject, but so much thereof as is common to it with the 
whole class of which it is one. Thus the concep- 
tion bright denotes, not all of any one bright object, 
but so much of it, as it has in common with all 
bright objects. 

13. This conception, or mental representation of 

what is common to a plurality of ob- Concrete and 

A^^tract Con* 

jects, may be abstract, or viewed by cep ti ns, 
itself irrespective of any objects to which it belongs, 
as brightness; or concrete, i. e. belonging to some 
object, as bright moon. 

14. It may also be considered subjectively and 
objectively, either with reference to the mental pro- 

almost as vaguely. Particularly they have used it to denote the 
mental similitudes of past cognitions or objects of cognition which 
are raised in the mind by the exercise of memory. As, when I 
remember a house, I have a mental image, or as these philoso- 
phers would say, a conception of it. So of the products of Con- 
structive Imagination — new combinations, which are not mere 
copies or images of any thing else. These, too, by many authors, 
of whom Reid is an eminent example, are styled conceptions. 
The strict scientific use of the term, however, in present philo- 
sophic nomenclature, is to signify the mental exercise or product 
of generalization. 



20 LOGIC. [Chap. I 

cess forming it, or with reference to the product of 
Subjective and that process, considered as formed, and 
ce^Ton™ Con- ma de the object of our thinking. Some 
wpt. writers limit the word " conception" 

{conceptio) to the former ; and denote the latter by 
the word " concept" (conceptus). And as logic, in 
evolving the laws of this product of thought, makes 
it the object of attention, these writers use the word 
" concept" exclusively to denote this, which is the 
primary element within this sphere of this science. 
Since, however, this word serves no purpose not 
equally well accomplished by the word "concep- 
tion," we shall adopt the latter to denote the first 
object-matter that falls within the sphere of the 
science of logic, i. e. the products of Abstrae- 
Generalization tion and Generalization ; of which, be it 

involves Ab- 
straction, observed, in passing, the former may 

take place without the latter, but not the latter 
without the former. 

15. Conceptions, and, indeed, the whole pro- 
Conceptions in- cess f generalization, are 'ncomplete, 

complete with- 
out names, fugitive, and unavailable, until they 

are set, and so to speak, encased and preserved in 

names. Each one may easily test this for himself, 

by an examination of his own consciousness. He 



Sec. L] ITS SPHERE AND OBJECTS. 21 

will see that he cannot retain, or employ, to any 
extent, in judgments and reasonings, the ideas ot 
conceptions denoted by general words, without the 
words themselves. The attempt to preserve and 
turn to account our generalizations without naming 
them, has well txen likened to the process of making 
conquests, and leaving them without fortifications 
for their security and preservation. 

16. Hence, as terms are so implicated with the 

conceptions for which they stand, we Terms and Con- 

ceptions inter- 
may often use the two interchangeably, changeable. 

The older logicians were wont more commonly to 
use the former when treating of this department of 
their science. Some, of whom "Whateley is a promi- 
nent example, have carried this view to 
, n . . . , T Extreme views, 

the extreme ot maintaining that .Logic 

is wholly conversant about language. This has 
been pronounced by others, as Hamilton, to be 
utterly groundless. The truth is, assuredly, that 
logic is primarily and properly conversant abont 
thought, and about language incidentally as the 
vehicle of thought. The science of language is 
Grammar, or Philology, and not Logic, which is 
the science of the laws of thought. 

17. And yet, owing to the inseparable conneo- 



22 LOGIC. [Chap. U 

tion, amounting, for practical purposes, to almost 
Sense in which au identification of thought and lan- 

Whateley's doc- 
trine is tme. g u &ge, there is a sense obviously, in 

which Whateley's doctrine may be regarded as a 

half truth — often the worst form of error.* 

18. The first part of Logic then has to do with 
The first part of that product of thought which results 

Logic deals with n tj» nt/^< i» 

Conceptions or from generalization, called Conception; 

Terms. and with terms or names incidentally, 

as being the vehicles of conceptions. 

The next of the Discursive Faculties is Judgment. 
And it gives as its products the second 
great object of logical science, to which 

we now proceed. 

Sect. II. Logical Judgments. 

19. We say Logical Judgments, because there is 

Logical and a sense in which judgment is a con- 
Primitive Judg- 
ment compared, stituent of every act of mind or exer- 
cise of consciousness. If we have a pain we can- 
not but judge that we have it. Consciousness is 
the knowledge of our mental operations, and in- 
separable from them. Of course, the knowledge 

* This interpenetration of thought and language may go far to 
reconcile and clear up the dispute between the Nomin Uists and 
Oonceptualists. 



Bee. II ] ITS SPHERE AND OBJECTS. 23 

that we have them, is in some sense, a judgment 

that we have them. For distinction's sake this, 

which enters into all the intuitions of the mind, 

may be called Primitive Judgment. It Primitive Judg- 

furnishes the materials out of which me *V * ts °^ 7 

predicate exist- 

conceptions and logical judgments are ence. 
ultimately framed. The only predicate which it 
gives is that of existence. It simply affirms that a 
given phenomenon external or internal is. 

20. Logical Judgment, on the other hand, in- 
cludes a conception as one, or concep- Logical Judg- 
tions as both, of its elements. It com- m(mt definedi 
pares two conceptions, or a conception and an in- 
tuition, and affirms that they agree or Compares Con- 
disagree. Thus it affirms of the con- ce P*°* s or °°»' 

° ceptions and In- 

ception "man" and the conception "ra- tuitions. 

tional," that they agree, ?'. e. that " man is rational." 
So likewise of horse and quadruped, tree and plant, 
etc., etc. Or if we take an individual object of in- 
tuition named Pompey, and the conception man, or 
horse, as the case may be, we may affirm that 
" Pompey is a man ;" " Pompey is a horse." And 
negatively, we may affirm that the conceptions man 
and quadruped do not agree ; " man is not a quad- 
ruped;" that the particular object called Pompey 



24 LOGIC. [Chap,!. 

and the conception, philosopher, do not agree. 
Pompey is not a philosopher. Similar examples of 
all these forms of judgments the reader can easily 
multiply at his pleasure. 

21. Remarking here provisionally, that a judg- 
Terms, Subject me nt consists of two parts or terms 

and Predicate 

defined, (termini, extremes) the Subject, or that 

which is spoken of, and the Predicate or that which 
is said of the subject, it follows from this defini- 
The Predicate tion, that while the subject may be 

always a con- 
ception, either an intuition or conception, the 

predicate must always be a conception or common 

term, the name of a class. If we have Peter for the 

subject, unless we have a common term- as predicate, 

we can get only the senseless tautological judgment, 

Peter is Peter. Of judgments it is unnecessary now 

to say more, in marking out the sphere of Logic, 

than that they constitute the second great product 

of thought, and object of Logic as the science of the 

laws of thought. 

22. From Judgments the mind proceeds to de- 

The mind pro- rive other judgments founded upon 

ments to new them. This is Reasoning, or inference 

judgments from premises to conclusion. Thus to 

founded upon 

them. conclude from premises is in fact to 



Sec. III.] ITS SPHERE AND OBJECTS. 25 

judge. So all modes of thought, from conceptions 
to reasonings are in reality forms of ^ thonght in 

. Teality a form 

judgment. The third and last great of judgment, 
province of Logic, therefore, is the laws of rea- 
soning. 

Sect. III. Keasoning. 
23. This runs into various branches or modes, 
Mediate and Immediate, Categorical Tlie tMrd P ro * 

vinceofLogicis 
and Hypothetical, which need not be Reasoning, 

further defined nor explained till we come to treat 
of it in form and in length. 

Until a recent period, it was largely the custom 
of logicians to treat Reasoning as constituting the 
whole primary object-matter of their Former place of 
science, and to bring Judgments and ^aflrea- 
Conceptions, under the name of Propo- tises. 
sitions and Terms, into the sphere of Logic, only 
on the ground of their being elements of the Syl- 
logism and other forms of reasoning. But they in- 
variably treated of these terms and judgments in 
many aspects of the first importance, which are not 
immediately essential to the Syllogism, or other 
forms of Reasoning. Thus Whateley has a short 
introductory chapter in explanation of terms (con- 
ceptions), so far as their relation to forms of reason- 



26 



LOGIC. 



[Chap. L 



ing is concerned, while he postpones the considera- 

Conceptions and tion of them in chief > tiU he has finished 

Judgments t } ie analysis of the various forms of the 

have a place in 

Logic in their Syllogism. This shows that these con- 
own ng t. ceptions and judgments have a separate 
and independent place in Logic on their own account, 
and in their own right, irrespective of their place 
in the Syllogism. This will be more evident when 
the student reaches these subjects. Indeed, it is only 
necessary to think of Genus, Species, Differentia, 
Essence, Accident, Absolute, Eelative, Correlative, 
etc., as applicable to Conceptions, to see that these 
have in their own right, a leading place in the 
science of Logic. The definition of Logic, till re- 
cently in vogue, as being the science of 
Reasoning, is therefore too narrow. It 
is, as we have defined it, and as the present masters 
of the science generally define it, 

Definition of I- THE SCIENCE OF THE LAWS OF 

**&*• Thought. 

II. Thought is the operation, or product 

OF THE OPERATION, OF THE DISCUR- 
SIVE Faculties, as distinguished 
from the Intuitive. 



Recapitulation, 



Of Thought. 



Sec. III.] ITS SPHERE AND OBJECTS. ■ 27 

III. The Discursive Faculties are, 
a. Abstraction and Generalization; the product 
of which is Conception. 

Enumeration of 

6. Judgment, which out of Concep- Discursive Fac- 
tions forms Logical Judgments. 

c. Reasoning which from judgments given evolves 
other judgments founded upon them. 

The thinking and products of think- Lo s ic deals 

° with Concep- 

iug, whose laws Logic unfolds, therefore, tions, Logical 

r« T T Judgments, and 

are, Conceptions, Logical Judg- Rea ° onings ', 
ments, Reasonings.* 

* I also rank Constructive Imagination among the Discursive 
Faculties. Its operations and products, therefore, are of the na- 
ture of thought. As we unfold the laws of thought, it will ap- 
pear that they cannot be violated, even in the creative works of 
this faculty. They may be violated in the apparent form, sound, 
and sense of the language employed, and the imagery constructed ; 
but not in its real interior significance. All appearance of thought 
which violates these laws, is not genuine thought, but a counter- 
feit or simulation of it. The creations of imagination cannot 
abolish the laws of Conception, Judgment, Eeasoning. They can- 
not legitimate contradictions, render a round-square possible or 
conceivable, or make arguing in a circle valid. If it tells us that 
rain-drops are the tears of the sky, it means such resemblance 
between the tears and rain-drops as actually exists. The laws 
of Logic, theiefore, so far as applicable to Constructive Imagina- 
tion, are developed in treating of Conceptions, Judgments, and 
Seasonings. 



28 LOGIC. [Chap.l 

Sect. IV. —Pure and Applied Logic* 

24. Having defined the sphere of Logic, and 
pointed out the matters with which it deals, it re- 
mains that we further elucidate it, by showing what 
it is in itself considered as pure science, in distinc- 
tion from the application of its principles to the 
investigation of truth and the ascertainment of facts 
— Pure and Applied Logic. 

Pure Logic treats of the Laws of Thought 
Pure Logic as they are in themselves, whatever be 

deals with the , . 

laws of Thought the object-matter to which they are ap- 
lrrespective of pXi e d, and irrespective of their applica- 

their Applica- # rr 

tions. tion to any case of actual being. Its 

principles and laws, like those of Pure Mathema- 
tics, are true in themselves, irrespective of their 
application to cases of actual being, nay, whether 
there be any actual being to which they are appli- 
cable or not. The laws of the Syllogism, the con- 
ditions of valid reasoning, the principles which 
determine genus, species, differentia, essence, logical 
division and definition, are the same, whatever be 

* This and the following chapter may be passed with advan- 
tage for the present, to be taken up as an introduction to Chapter 
VI. on Applied Logic. A 






6ec. IV.l ITS SPHERE AND OBJECTS. 29 

the objects to which they are applied, whether 
angels, men, animals, plants, or grains of sand; 
and aside of such applications. 

In this Logic classes with Mathematics, and with 
strict Metaphysics. The rules of Arith- it classes with 
raetic, and the propositions of Geometry ^ UTe T-^T' 
are true, irrespective of their applica- physics. 
tions to actual being, and in respect to whatever 
kinds of actual being furnish the conditions to which 
they are applicable. The Multiplication table is 
true in itself, irrespective of any actual being, and 
in regard to all actual being to which it is appli- 
cable. 12X12 = 144. This of itself, however, does 
not prove any truth of actual being. It does not 
prove that there are twelve persons, each twelve 
years old. But it does prove, that if there are 
twelve such persons, their aggregate age is 144 
years. Logic, as such, does not concern 

. . t n .,1,1 • • i n Does not in it- 

itself with the original sources of our self give origi . 
knowledge of actual being, or of the nal knowledge 

of actual being, 

conditions to which it applies. These 
may be supplied by intuition, or testimony, or legit- 
imate logical deduction from them. They may, in 
various aspects, come within the province of Psy- 
chology, Metaphysics, Ontology, or the different 

3* 



30 LOGIC. [Chap. . 

departments of physical science. But from what- 
ever sources the requisite conditions of actual being 
are furnished, to which any of the principles of 
Logic apply, the corresponding consequence neces- 
sarily follows. Logic does not prove that gold is 
fusible, or that gold is a metal ; but given these 
truths from whatever source, and it follows that 
some metal is fusible, on principles of Logic. 

25. Hence, pure Logic, like pure Mathematics, is 
a science of necessary principles or 

It is a science ,, -^ - . 

of necessary truths. By necessary we mean that 
tmths, "Neces- ^ opposite of which, the mind cannot 

sary" defined, 

conceive to be true without intellectual 
suicide. Such are the following, " that the whole 
is greater than a part," that " all qualities must 
belong to some substance," that " no two straight 
lines can enclose a space." So, as in the proper 
place the student will more fully see, that there can 
be no valid conclusions in a syllogism vitiated by 
negative premises, illicit process, or undistributed 
middle ; that every relative supposes a correlative, 
that we may predicate of a species its genus and dif- 
ferentia ; these, with all other laws of pure Logic, are 
necessary truths. They are not only true in parti- 
cular cases, but, when understood, it is seen that 



Sec. IV.l ITS SPHERE AND OBJECTS. 31 

they must be true, as the rules of Arithmetic and the 

propositions of Euclid must be true in all 

-P-.. T . . , Logic the sci- 

cases. Hence pure Logic is not only, as ence of the ne . 
before shown, the science of the laws, cessary laws of 

; ; Thought. 

BUT OF THE NECESSARY LAWS OF 

THOUGHT. 

26. This characteristic classes Pure Logic with the 
a priori, as distinguished from the a Pure Logic an a 
posteriori sciences. By a priori know- P norl scleilce ' 
ledge is meant that which is known from conditions 

given, without needing: verification from 

fe > i Definition of a 

experience. A posteriori knowledge priori and a pos- 

j -i n r* teriori. 

depends upon experience tor proot. 
The axioms and propositions of Geometry are a 
priori, because they are known and proved inde- 
pendently of experience. The physical and induc- 
tive sciences, on the other hand, are a posteriori, 
because they are dependent on experience for proof. 
Hence, all sciences of necessary truth, including 
Logic, are a priori, for they not only show what ex- 
perience has proved true ; but what ever must be 
true in all possible experience, and must condition 
that experience. AVe know a priori, that no two 
straight lines can enclose a space, and that every 
equiangular triangle must be equilateral. So we 



32 LOGIC. [Chap. 1. 

kno\t, as the student in the proper place will see, 
that, as the Extension of a conception increases, its 
Intension must diminish, and vice versa : and that 
there can be no conclusion from negative premises. 
27. It is putting the same thing in another light, 
to say that the laws developed by Logic, are those 
which are necessary to the very form of 

Logic deals 

with the Porms thinking, whatever be the subject-mat- 
nff * ter about which we think, and indepen- 
dently of such subject-matter. The forms of think- 
ing in Conceptions, Judgments, and Reasonings, 
are the same, whether applied to planets or to 
worms ; just as the forms of Arithmetical Addition, 
Subtraction, &c, are the same, to whatever they 
may be applied : and the opposite sides of a paral- 
lelogram are equal whether it be on wood, slate, 
iron, or between lines imagined in pure space. 
This truth is set forth by saying that Logic is the 
science of the forms of thought ; or of the formal 
laws of thought — either phrase will serve our pur- 
pose sufficiently well. And so combining all the 
elements thus far shown to be comprised in the 
essence of Logic, we reach this definition : Pure 

Completed defi- L ° GIC « THE SCIENCE OF THE KECES- 
nition of Logic. SARY AND FOBMAL LAWS OF THOUGHT. 



Sec. IV.] ITS SPHERE AND OBJECTS. 33 

Those sciences, the Mathematics, Logic, and, with- 
in certain limits, Metaphysics, which other Formal 
deal with truths, not within themselves Sciences ' 
originally implying actual being, but which are 
forms regulative of such actual being as presents 
the conditions to which they apply, are called 
Formal Sciences. Those on the other hand which 
have what, in these relations, is called Fom content 
Content, or matter of actual being, Matter - 
whether in the realms of body or spirit, are called 
Material Sciences. The contrast here Material Scien- 
is not between Material and Spiritual, ceSt 
but between Material and Formal. The opposite 
of Spiritual is Physical Science. Mat- 
ter and Material in these connections gp^i^ai a ig 

refer to substances and phenomena of t0 Physical Sci- 
ences. 
actual being, whether bodies or spirits. 

Accordingly, pure Logic is one of the Formal 
Sciences. 

28. These are also sometimes named Hypotheti- 
cal Sciences ; because they prove truths „ , , 

' J r i Hypothetical 

of actual being only on the hypothesis, Sciences ex- 

that the conditions of actual being are 

given to which they are applicable. Thus, that the 

angle in a semi-circle is a right-angle proves no 

C 



34 LOGIC. [Chap. L 

fact of actual being, until we have some substances 
in the form of a semi-circle, with an angle inscribed 
in it. Such an angle we know must be a right 
angle. 

Sect. V. — Applied Logic. 

29. In the actual investigation of truth, we must 
go beyond Pure Logic, which, of itself, like Mathe- 
matics, deals only with forms of thought, and has 
Pure Logic a no con tent of actual being. Yet, like 
calculus. Mathematics, it is of the utmost value 

as an instrument or calculus in the investigation of 
truth. The primary facts, which lie at the basis of 
astronomical science, were not obtained by mathe- 
matics but by telescopic observation. Mathematics 
is an instrument for determining what is fairly in- 
volved in, or results from these facts so observed. 

Application of ^ ^ s use ^ e f° rmer science has made 
Formal Scien- the immense strides which have ad- 
ces to facts a , . . 

means of dis- vanced it to its present perfection. So 
coveringtmths. Geometry and Trigonometry will not of 

themselves make a science or art of Navigation, 
Surveying, or Engineering. They cannot furnish 
the facts w T hich underlie these sciences. But the 
application of these Mathematics to facts otherwise 



Bee. V.] ITS SPHERE AND OBJECTS. 35 

discovered, is indispensable in these sciences, and 
alone makes them possible. 

30. So is it with the laws of Thought unfolded 
by Logic. They do not, of themselves, prove any 
original fact of existence ; but, given such data, as 
are furnished by other means, it is an instrument 
for showing what is and what is not fairly contained 
in them : for unfolding explicitly what is involve! 
implicitly: for guarding us against un warranted 
conclusions from given facts or truths ; 

for guiding us to the avoidance of fruit- 
less, and the adoption of fruitful methods of inquiry 
in the realms of actual being. Such use of the prin- 
ciples of Logic in assisting us to right, and pre- 
serving us from wrong processes of thought in 
our search after truth, is what is meant A plied Lo io 
by Applied Logic. This has two de- defined. 
partments. 

31. a. The doctrine of Fallacies. Showing 

the various ways in which men consciously or 

unconsciously employ, a mimicry of 

thought, especially of reasoning, for the ^^ffi 

things themselves, thus sometimes im- cies *&& Me- 
thod, 
posing upon themselves, or essaying to 

impose on others. 



36 LOGIC. [Chap. L 

b The doctrine of Method, or the right way 
to ascertain the truth, by modes of investigation, 
not contrary to, but harmonious with the laws of 
Thought. 

32. Pure Logic then treats of the formal and 
necessary laws of Thought in Conceptions, Judg- 
ments, and Reasonings. Applied Logic deals with 

the application of these laws to the de- 

Snnnnation, m m 

tection of Fallacies, and the develop- 
ment of a proper Method for the investigation of 
Truth. Before proceeding, however, to the formal 
consideration of each of these topics, we will make 
a few r preliminary observations, first on the utility 
of the study of Logic, and secondly on the funda- 
mental principles or axioms of the science. 

Sect. VI.— Utility of Logical Study. 

33. The study of Logic is useful as a means of 

disciplining and invigorating: the mind. 

tfses of Logic. . & & 

intellectual Few studies more effectually promote 
iscip me. habits of attention, discrimination, and 
continuous application. 

34. The knowledge thus acquired is of high 

Imparts vain- va ^ ue OU its own account. All knOW- 
ftble knowledge, ledge is precious and elevating; but es- 



Bee. VI.] ITS SPHERE AND OBJECTS. 37 

pecially that which sheds light on the laws of our 
thiuking, our intelligent and rational nature. 

35. It is invaluable as furnishing the nomencla- 
ture, the Technical Terms, which define 

Furnishes apt 
the products and relations of true Technical 

Thought, and the nature of the fallacies 
which counterfeit it. The possession of these names 
in a multitude of cases will instantly suggest to the 
mind the clew to difficulties which would otherwise 
perplex it. The very terms, genus, differentia, peti- 
tio principii, ignoratio elenchi, arguing in a circle, 
will of themselves often suggest an analysis or ex- 
planation of perplexities which otherwise might 
long be insoluble. 

36. Generally, as a guide to right, and a pre 
ventive and corrective of spurious QtLide to ^ 
thinking,^ e. of the aimless, erratic, and Thinking, 
abortive exercise of our faculties. So it is a pro- 
paedeutic to all other sciences. It furnishes a 
needful training for every department of study. So 
it has been crowned by some, as scientia scientiarum } 
by others, as ars artium. 

37. The question has been much discussed whether 
Logic is a Science or an Art. But as Logic a Science, 

and Gnide to 
the end of Science is to know, and of Art. 

4 



38 LOGIC. [Chap. L 

Art to do, or rather to make a product which sur- 
vives the making, so there can be no doubt that 
pure Logic is, like pure Mathematics, properly a 
Science; while Applied Logic, like Applied Mathe- 
matics, may afford great light in the learning and 
executing of the arts to which it is applicable, as 
the art of Eeasoning, Rhetoric, and Oratory. Al- 
though not useful as in itself an art, it is useful as 
furnishing light and guidance in the noblest arts. 
38. The study of Logic as the science of the Laws 
of Thought, gives, in fact, if not in form, 
clioiogy'of Bk- the knowledge of Psychology, so far as 
cursive Facul- t ^ e f acu lties of Thought are concerned. 

ties. ° 

Although the necessary and formal laws 
which all true Thought must obey, are not of them- 
selves psychological phenomena, yet it is impossible 
to master them, in their application to the pheno- 
mena of the Discursive Faculties, without so far 
forth understanding the psychology of those faculties. 
So far as Abstraction, Generalization, Conception, 
Judgment, Reasoning, are concerned, little remains 
to be learned, which is not acquired in a thorough 
course in Logic, in the present acknowledged scope 
of that science. It is easy for the teacher, with little 
addition of labor, to compass this portion of psycho- 



Bee. VI.l ITS SPHERE AND OBJECTS. 39 

logy, in connection with his regular course in Logic 
— a matter of some moment, in view of the scanty 
time generally allowed to those subjects. 

39. It has indeed been said that men reason, 
whether they know Logic or not. They are not 
dependent on Logic to confer on them the 

Objections of 

power of reasoning. Even Locke is Locke and 
guilty of such poor burlesque on this ot ersre te 
high subject, as the following. " God has not been 
so sparing to men to make them barely two-legged 
creatures, and left to Aristotle to make them ra- 
tional. . . . God has been more bountiful than so ; 
He has given them a mind that can reason wdthout 
being instructed in methods of syllogizing," etc.* 
This is quite as relevant, as if one should say, "God 
has not been so sparine: of gifts to men, , % 

r & & ' Analogy of 

as to leave it merely to the gramma- Grammar and 
rians to confer the gift of speech, or to 
the rhetoricians to confer the gift of composition 
and oratory." The science of Grammar, of course, 
does not confer the gift of speech. It presupposes 
that gift. But that it helps to the correct use of 
language, who will dispute ? Ehetoric does not first 

• Quoted by Whateley— Logic. Harper's Edition, p. 37. 



40 LOGIC. [Chap. 1 

make men eloquent; but who can doubt that, rightly 
used, it will greatly augment this gift of elo- 
quence in those naturally endowed with it ? Logic 
does not impart the power of reasoning or thinking. 
But who will question that it greatly assists in de- 
tecting and avoiding the spurious counterfeits of 
them ; and that it is every way a great intellectual 
tonic? Locke is not alone, even among men of 
mark in philosophy and literature, in 
this vulgar and Vandal disparagement 
of Logic, which, if admissible against this, is valid 
against all liberal study, discipline, and culture. 
No less a man than Macaulay has allowed himself 
to indulge in reflections and implications of like 
force and effect in regard to Grammar and Rhetoric 
as well as Logic* 

Sect. VII. Fundamental Principles or Axioms of 
Logic, from which all its Particular Laws Flow, 
or by which they may be tested. 

40. These are commonly reduced to the four 
_ „ „ following; — Identity, Contradic- 

The Four Fun- & ' 

damentai Prin- TION, EXCLUDED MIDDLE, AND SOF- 

Clpes * ficient Reason. 

* See Essay on Lord Bacon. 



Sec. VII.] ITS SPHERE AND OBJECTS. 41 

I. The principle of Identity, which amounts 

simply to this : that we may affirm of 
i . ii ii Identity, 

objects that they are what they are. 
This lies at the foundation of all Positive Concep- 
tions, and Affirmative Judgments, and Reasonings. 
Thus if the Conception rational be a part of the 
Conception man, we may affirm that " man is ra- 
tional." On the same ground, we may have the 
Conception " rational animal," because these may 
concur in the same being. 



&• 



II. Contradiction. That is we may not 
affirm the co-existence of Conceptions 

., - ,., Contradiction. 

or attributes that are mutually contra- 
dictory, as "round-square," "triangular parallelo- 
gram," " good wickedness." 

III. Of two contradictories one must ^ , , , v . . 

Exclnded Mid- 

be true, and the other false. There can die. 

be no medium between these. This is the Law of 

Excluded Middle. 

IV. For every conclusion, affirmation, or nega* 
lion, there must be a Sufficient Rea- g^^ ^ ea . 
son or Ground. It must be evinced son - 

by self-evidence, or other sufficient evidence. 

4* 



42 LOGIC. [Chap.1. 

41. These principles may seem too obvious and 
Importance of familiar to be the foundation of any 
these principles, important science. But we must bear 
in mind, that the highest sciences are but develop- 
ments from a few simple elements or axioms. The 
science of Mathematics is but a development 01 
evolution of a few axioms as simple as the fore- 
going. Herein, very largely, lies its adamantine 
strength. What are the laws which keep the myriads 
of orbs harmoniously circling in the depths of space, 
but developments and applications of the simple 
but great law of gravitation? And does not the 
highest of authorities teach us that, on the simple 
obligation to love God with all the heart, mind, 
soul, and strength, and our neighbor as ourselves, 
" hang all the law and the prophets ?" That is, 
that all the details of religion and morals, are but 
the logical unfoldings of this simple principle ? 



CHAPTER II. 

Section I. — Conceptions. 

1. In unfolding the nature of Conceptions, as 
also, of Judgment and Reasoning, it will be ne- 
cessary occasionally to repeat a few things, which 
were unavoidably introduced by way of anticipation 
in our brief preliminary exposition. 

2. Conceptions stand contrasted with Intuitions, 

which cognize single presentations, m 

° x Conception and 

whether external or internal, whether Intuition com- 
bodies or states of consciousness, im- 
mediately and intuitively. Conceptions, on the 
other hand, grasp (con-capio) a plu- 
rality in one, through the medium of grasps a plural- 
a common sign or mark, whereby l y m one ' 
they are, so far forth, represented. This plu- 
rality may be of objects thus brought to This plurality 

... i may be either 

unity m a common genus, by a common of J ob . ectg oJ 
mark or resembling quality, as the marks, included 

under a common 

whole class of red things are brought name. 

43 



44 LOGIC. [Chap. 1L 

to unity, or classified by the common mark of red- 
ness. Or it may be a plurality of marks or attributes 
under one name. As hexagon includes the two 

Ex ressed by a mar ^ s ; rectilineal figure and six sides. 
"General Word. Another aspect of the same truth is, 
Conception is that act or product of the mind which 
is expressed by a General Word. And hence, 
3. Conception is that product of the mind which 
results from Generalization, whereby many 

Formal Defini- / ' . v J 

tion of Concep- individuals are combined in one class, 
through one or more similar qualities, and 
are indicated by a common term. Thus, certain 
pieces of iron-ore are observed to have the property 
of attracting iron, and are generalized into one class 

T . ., under the name Magnets. It is obvious 

Involves Ad- ° 

straction. that, in attending to this quality of at- 

tracting iron, exclusively of others, there is a with- 
drawing or abstracting it from them. Here is 
Abstraction. There is Comparison, in 
ompanson. or( j er t detect the resemblance of these 
qualities in the several magnets. Then there is the 
Classification or Generalization by vir- 
tue of this resemblance. Finally, in 
order to complete and guard the product of this 
process, the name " Magnet " is applied to this class. 



Sec. I.] CONCEPTIONS. 45 

This is Denomination. Thus we have a conception 

formed as the result of Abstraction, Com- 

. . Denomination. 

parison, Generalization, Denomination. 

4. Notion is a term of wider import than Con- 
ception. It is used almost as loosely Motion. 

as Idea. It includes representations Idea ' 

not only of Conception, but of mental similitudes of 

objects remembered by simple Imagination. 

5. Conceptions and the corresponding terms 
which express them, may be viewed either as, 

Abstract, 

i. e. as expressing a quality irrespective of any object 
in which it inheres, as Magnetism, Heat, ^ stract c 
Wisdom, Virtue. Or they may be viewed ceptions. 
as, 

Concrete, 

t. e. as inhering in some object, as magnet, hot-blood, 
wise man, virtuous person. These dis- 

.,, . Concrete, 

tinctions will also apply to the inherence 
of higher in lower conceptions, as will be seen when 
we come to define this distinction. They also pre 
pare us to understand the distinction between Den/ 
tative, Connotative, and Non-Connotative terms. 



46 LOGIC. [Chap. II 

6. A Term is Denotative in so far as it denotes 
an object or objects. All names of single objects, 
Denotative *" 6 * lingular Terms, have this capacity, 
Terms. Singn- whether they be proper names, or com- 

lar Terms. . .. . , . . , , . . 

mon terms with an individualizing par- 
ticle; as "John," "this man." All strictly concrete 
terms, as fools, stones, trees, have this capacity, 
besides their power to connote. Abstract concep- 
tions have not this capacity. They include quali- 
ties but not objects, as virtue, color, wisdom. 

7. Connotative (which are also Attributive), terms 
Connotative or conceptions denote objects, and con- 
Attributive. nQ ^ Q q Ua Uties along with them, as men, 
roses, animals. Such are all Adjectives, inasmuch 
as they express qualities belonging to the objects 
indicated by the names to which they belong. The 
Adjectives foolish, organized, etc., can only be used 
in reference to their appropriate objects. When, 
however, adjectives are used to qualify abstract 
nouns, they denote not so much objects, as the 
quality which they still further determine. Thus, 
"great virtue," "scrupulous veracity." Of course, 
all concrete common nouns, as horses, quadrupeds, 
etc., are connotative. They cfenote objects and con* 
oote qualities. 



Sec. II.] CONCEPTIONS. 47 

8. Non-connotative words are proper nouna 
which denote objects simply; also ab- Non . 0ollIlota . 
stract common terms, which denote qua- tative - 
lities (and in this sense have denotative power), but. 
connote no objects; as blackness, harmony, etc. 
Proper names ordinarily denote intuitions or sing]« 
objects, not conceptions. 

9. Proper Names sometimes acquire the attributes 
of common terms, when the individuals ^ 

; Proper Namsa 

they denote become types of a class, become com- 
As when we speak of a Webster, a Wash- 
ington, a Napoleon, or of the Csesars and Nimrods 
of our race ; i. e. the class of men who have the 
qualities of Caesar or Nimrod. In such cases, these 
names are connotative. Adjectives formed from 
them are like other adjectives in this respect, as 
British subjects, a Websterian or Johnsonian style, 
i. e. a style having the qualities of the style of these 
authors. 

Sect. II. — Higher and Lower Conceptions. 

10. It is evident that the same process of gene- 
ralization may be applied to classes as Generalization 

to individuals. Thus triangles, squares, ° casses , as 

& ; *■ 7 well as mdi- 

parallelograms, polygons, etc., may all vidnals, 



48 LOGIC. [Chap. IL 

be generalized into the one class of rectilinear 
figures. Circles, ellipses, parabolas, etc., may be 
reduced to the one class, curvilinear figures. Recti- 
linear and curvilinear again may be united as one in 
the higher genus, plane figure. Dogs, lions, horses, 
etc., may be generalized into the higher class of 
quadrupeds. And so of numberless examples which 
will readily occur to the student. Now in such 
cases, the broader conception which includes the 

Higher andlow- ° therS > is Called the Hi g her - The nar ' 

er Conceptions, r0 wer ones which are included, are the 
Lower. Quadruped is a higher conception than 
dog or fox. As the process of combining lower 
conceptions into a higher, by laying aside their dif- 
ferences, is Generalization ; so that of resolving the 
higher into the lower, by adding on these differences, 
•n . . .. is called Determination. The Concep- 

Determmation -*- 

of Conceptions, tion triangle undergoes this process when 
it is resolved or determined into equilateral, isosceles, 
and scalene. 

11. In the scale of higher and lower Conceptions 
we have another application of the 

Conciete and 

Abstract ap- distinction of the Concrete and the Ab- 
p e o asse >, g ^ mc ^ j^ high^ Conception which is 

Abstract when taken by itself alone, becomes Con- 



Bee. III.] CONCEPTIONS. 49 

crete when incorporated with another in a lower 
Conception. Thus the Conception rationality is 
Abstract, when taken by itself alone, but when 
united with animality it becomes Concrete in the 
lower Conception manhood. 

Sect. III. — Genus, Species, Individual, Differentia, 
Essence, Accident, Property. 

12. In any series of higher and lower Concep- 
i ons, each higher is a Genus to those 

Genus. 

next below it, out of which it is formed 
by generalization. Those next below it are its 
Species. Thus birds, fishes, beasts, rep- 
tiles, men, are species to the Genus 
animal. Differentia, or Specific Difference, is the 

mark or quality which distinguishes 

^ J & Differentia or 

one species from others under the same Specific Differ- 
Genus. Individual or Intuition is that ence ' 
which is logically indivisible, although it may be 
capable of physical division. It can- 

. Individual. 

not, therefore, be a species, although it 
may be one of the constituents of a species. An 
ox cannot be divided logically, but may be physi- 
cally into hide, horns, quarters, etc. But then it is 
no longer an ox. Of course then an individual can 



60 LOGIC. [Chap. II 

nevei be a Species or Genus, which is always com- 
_, . _ posed of a plurality of individuals. Es- 

Essence is Gen- * r J 

ns and Differ- sence refers to Species, and its essential 
constituents, i. e. its Genus and Differ- 
entia. These are called Essence, because when 
present the Species is present ; if either be absent 
Logical Defini- ^at * s wanting. These which consti- 
ti 011 * tute the Essence of a Species, also con- 

stitute Logical or Essential Definition. As rose 
(Genus), red (Differentia), constitute the Essence or 
Definition of red-rose. Accident, or Accidental 

Conception belongs to a part, and not 

Accident. 

to the whole of a class, as sickness or 
health to man. Property belongs to the whole of 
a Species, but is not a part of its Essence : as liability 
to laugh, or grow gray, in man whose Essence is 
(Genus) animal, (Differentia) rational. Where these 
are, whatever else is wanting, there is manhood. 
Where they, or either of them, are not, there man- 
hood is not. 

Sect. IV. — Subaltern and Proximate Genera and 
Species. Summum Genus and Infima Species. 

13. In a series of higher and lower Conceptions, it 
has been shown that the same one may be a Genus 
to those next below, and Species to that next above, 



Bee. IV.] CONCEPTIONS. 51 

Those Species to which any given Species becomes a 
genus, are relatively to it Subaltern gubalterii ^ 
Species. Those Genera which are Species ^ s and Species, 
of a higher Genus are called Subaltern Genera. 
Thus White-oak, Yellow T -oak, Live-oak, etc., are 
Subaltern Species to oak, which is a Species of the 
genus tree ; and is therefore a Subaltern Genus to it. 
Summum Genus is that highest class g mnmiim Q eil 
which is never a species. Infima Species Infima Species. 
is that lowest class which is never a Genus. 

14. Proximate Genera and Species are those 
which are next to each other in order of pr^^e Q en . 
ascent or descent. Thus triangle is the era *&& Species. 
Genus proximate to equilateral, isosceles and scalene 
triangle. They are proximate Species of triangle. 

15. It should be noted that Summum Genus may 
be Absolute, with reference to the Uni- 

Absolute Sum- 
Verse, in which case it is Thing or mum Genus. 

t> • • l • j_ i t> i j • Relative also. 

.Being simply ; or it may be .Relative to 

a particular department — as animal is Summum 
Genus of corporeal beings having life and conscious* 
ness: plane superficial figure with re- 
ference to triangle, square, etc. And Summum Genus 

& ' ^ andlnfimaSpe- 

it is sometimes fixed arbitrarily with cies often arbi- 

n . . i n . • trarily fixed. 

reterence to the purposes of some parti- 



52 LOGIC [Chap. II 

cular discussion. Infima Species is also often diffi- 
cult to be fixed, for it is often hard to find classes 
that have no sub-classes. It might be supposed 
that isosceles triangle was Infima Species among 
plane superficial figures. Yet it may be divided 
into those of different magnitudes : and each of these 
again into those drawn on slates, boards, paper, etc. 
This therefore is seldom reached absolutely. It is 
rather fixed somewhat arbitrarily with reference to 
the exigencies of the inquiry in hand. 

16. It is important to note the difference between 
Lo i aland IT - Species ^ n Logic and in Natural History, 
turai Species In Logic, as has been shown, it means 

distinguished. . 

one oi the proximate lower classes into 
which any higher class or genus may be divided. 
The same class may thus be Genus to a lower, and 
Species to a higher. 

In Natural History, however, Species means only 
such a class of animals as has, or might have de- 
scended from a single pair, and the varieties of 
which may permanently inter-propagate among 

themselves. These sub-species are by 

"vfLTlSlilPS 

the Naturalists rigidly named Varieties. 
Bull-dog, terrier, grey -hound, etc., are Varieties of 
the Species, dog. 



Sec V.J CONCEPTIONS. 53 

In a Logical sense, quadrupeds, reptiles, birds, 
fishes, are species of the genus animal. In the 
Naturalistic sense, though they include Species, they 
are not themselves Species at all, as they want the 
marks already noted, of actual or possible descent 
from a single pair, and of inter-propagation. We 
are aware that some naturalists adopt other criteria 
of natural species. This, however, is not the place 
for extended discussion of that question. 

Sect. V. — The Three Powers of Conception. Exten- 
sion, Intension, and Denomination. 

17. From the analysis already given of the forma- 
tion of Conceptions, it appears that they Extension of 
include a plurality of objects through Conceptions. 
their resembling qualities indicated by a common 
name, and that the number of objects so included, 
increases with the height of the Conception. Thus 
man includes more objects than poet, orator, philo- 
sopher ; and animal more than man. This power 
to denote objects constitutes the Extension of Con- 
ceptions. 

It is equally plain that every conception in- 
cludes or connotes qualities or marks, intension or 
The ground of classification is resem- Comprehension, 

5 * 



54 LOGIC. [Chap. II 

bling qualities. Therefore the conception of any 
class involves these similar qualities or marks which 
constitute it. Thus the conception square involves 
the following marks : 1. Rectilineal figure: 2. Having 
four sides : 3. And those sides equal : 4. And its 
angles right angles. The conception man involves 
the marks, 1. Animal, 2. Eational. This power 
of conceptions constitutes their Intension, formerly- 
called their Comprehension, which by Whateley has 
been identified with Extension.* 

It is not less clear that conceptions have the 

capacity to receive names, and must re- 
Denomination, ., . , . , ., , 
ceive them m order to be preserved and 

used. A conception without a name, is like an un- 
fenced crop, or a volatile odor. This is the power 
of Denomination. 

To these three powers of Conception, three im- 
portant processes respectively correspond, viz. : Divi- 
sion to Extension ; Definition to Intension ; and 
Explanation to Naming or Denomination. 

* See Logic, Harper's Edition, p. 152. 



Sec. VI.] CONCEPTIONS. 55 



Sect. VI. — Inverse Katio of Extension and Intension, 
or Comprehension. 

18 As the Extension of Conceptions increases, 
their Intension diminishes. It is by . „_, . 

J As Extension 

laying aside the distinctive marks of increases, In- 

, .i.i tension dimin- 

lower conceptions, that we rise to higher, ifllieSi 
that is, more extensive conceptions. 
Thus by laying aside the distinctive marks, Equi- 
lateral, Isosceles, and Scalene, we arrive at the 
higher conception, Triangle, which has greater exten- 
sion, and less intension than isosceles, or scalene 
triangle. So poet, orator, statesman, 
have less extension and greater intension 
than man. The ratio of these to each other, there- 
fore, is inverse. Conceptions then may be regarded 
as embracing or constituting the respective wholes 
of Extension and Intension, each of which decreases 
as the other increases. Of course in Summum Genus 
Extension reaches its maximum, and Intension its 
minimum ; and conversely in Infima Species. These 

wholes have sometimes been called re- 
Logical and Me« 
gpectively, the former Logical, the latter taphysical 

Metaphysical . We agree, however, with ° e ' 

Hamilton, that this distinction is without any suffi- 



66 LOGIC. [Chap. Q 

cient ground, each alike being, in one aspect Logical, 
and in another Metaphysical.* 

Sect. VII. — Denomination. 

19. The process of Denomination keeps pace alike 

with the Extension and Intension of 

Names keep Conceptions. Thus, as the extension is 

pace with the x ' 

Extension and increased, names are employed to denote 

Conceptions. eac ^ en l ar g e d class, till we reach the 
highest, which is Being or Thing. And 
vice versa; as we add on successive marks to Being, 
names are applied to include or connote them, till 
the term man includes being, with life, sensation, 
and reason. All this is well illustrated in the fol- 
lowing tabular examples from Thomson's Laws of 
Thought, which we copy, because it is hard to find 
or invent any other, in all respects so much to the 
purpose. 

* Various other modes of expressing this double capacity of a 
Conception are in vogue. Thus a Conception viewed as an 



Extensive Whole, 


Intensive Whole. 


has 


has 


Extension, 


Intension or Comprehension, 


Breadth, 


Depth, 


Sphere, 


Matter, 


Objects, 


Marks, 


Power to Denote, 


Power to Connote* 



Sec VII.] 



CONCEPTIONS. 



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58 LOGIC. [Chap. II, 



Bect. VIII. — Varieties and Characteristics of Concep- 
tions USUALLY EXHIBITED WITH RESPECT TO THEIR DE- 
NOMINATION, or the Names which Complete and Indi« 

CATE THEM. 

20. As Conceptions are incomplete till they are 
, . , named, and these names are called 

Yarious kinds 

01' Terms mark- Terms, or Nouns, so certain features of 
53Ti Conce P tions are usually set forth as 
Conwjrtions. belonging to these terms or nouns. 
But tts these terms stand for Conceptions, so the 
different kinds of Terms are but different kinds of 
Conceptions, save in those exceptional cases of 
proper names, in which they denote only intuitions 
or individuals. 

21. The first division of nouns is into Proper, 
Proper, Com- Common, and Singular. Proper names 
mon, Singular. d eno te individuals merely, without con- 
noting any marks or qualities. Common names 
denote conceptions, and the objects included in them, 
together with their common marks, i. e. their exten- 
sion and intension. Singular terms denote single 
objects by means of a common noun, having its sig- 
nification limited by an individualizing particle, as 
this man, a house, some animal. 



Sec. VIII.] CONCEPTIONS. 59 

22. The second principal division of noons is into 

Attributive and Substantive. Attribu- 

, t „ ^ Attributive, 

tives are the adjectives of (jrammar. 

They express qualities not in the Abstract, but in 

the Concrete, as belonging to some substance. They 

express the attributes of Nouns, and are therefore 

used only in connection with the Nouns of which 

they are adjuncts. Substantive Nouns de- 
Substantive. 
note objects or abstract qualities, to which 

Attributives may be applied. Thus tree and hard- 
ness are Nouns Substantive. High and great are at- 
tributives which may be respectively ascribed to them. 

23. Another distinction is that between Distri- 
butive and Collective Nouns. A Noun 

, • Distributive. 

is Distributive or used distributively, 

when it is applicable to each and every individual 

included under it. It is Collective, or 

Collective. 

used collectively, when it is applicable 
to the whole, or a plurality only, but not to each 
and singular of the objects included under it. Thus 
man is a Distributive, and crowd a Collective Noun. 
Soldier is a Distributive, army a Collective Noun. 
The same noun may, however, be used both collec- 
tively and distributively. When we say, " these trees 
are oaks," trees are used distributively. When we 



60 JjOGIC. [Chap. IL 

say, " these trees amply shade this park," they are used 
Distribution of collectively. Hence a Term is said to 
Terms, be Distributed, when it is so used as to 

include all the objects signified by it distributively ; 
that is, all and singular of them, not merely a part 
of them, nor the whole of them collectively. When 
we say, "all men are mortal," men is Distributed, 
If we say, "some men are poets," men is not 
Distributed; and if we say "all men number 
1,300,000,000," men is not Distributed: for although 
all men are spoken of, it is not all and singular, but 
all taken collectively, that are meant. 

Terms or Conceptions are Absolute and Rela- 

Absolnte and ^ive. Absolute are irrespective of any 

Relative. other, as stone, tree. Relative are those 

which imply others. As son implies a parent, and 

king a subject. A pair of relatives like 

father and son are called Correlatives. 

In all Relative Conceptions there is a ground of 

Ground of Rela- *k e relation (fundamentum relationis). 

tion. j n ^q case f ki D g an d subject, it is 

government. In that of father and son, brother, 

sister, etc., it is the family. Some relatives imply 

, not merely one, but two, or even several 

Cases of several J ? f 

Correlatives. Correlatives. Thus, cousin implies not 



Sec. VIII.] COXCEFTIOXS. 61 

only another cousin, but parents, one of whom is 
brother or sister of one of the parents of the other 
cousin. 

24. Contrary and Contradictory Terms or Con- 
ceptions. Contraries are the most op- 
posed that can possibly belong to the 
sarue subject, as wise and foolish, soft and hard- 
Contradictories are simple Negatives of 
each other, and between them include 
all being actual and possible. Thus, man and not 
man, Ego and non-Ego, are pairs, each of which 
comprises the universe, not only of actual, but of 
possible being. And of such a pair of Conceptions 
one only marks out any definite class of Definite and In- 
objects. They are for this reason called defimte ' 
Definite and Indefinite Conceptions. Of the two Con- 
ceptions, man and not-man, the former alone contains 
any thing definite or positive either as respects ob- 
jects or qualities. The latter is not only indefinite, 
but essentially infinite. It embraces all the possi- 
bles but man, the subtraction of which does not 
make their number less than infinite, i^iutatea Con- 
Hence such purely Negative Concep- ceptions. 
fcions are sometimes classed by logicians as Infmi- 
tated Conceptions. 

6 



62 LOGIC. [Chap. .* 

25. It is not, however, true of most Negative 
Most Negatives Conceptions, that in their real and 
deL^efo 7 ! £ customar y significance, they have this 

nites. infinity. Especially is this not true of 

Attributives. Thus, if we speak of unkindness, 
we do not mean every thing that is not kind, but 
we mean the absence of this quality in intelligent 
and moral beings who ought to be kind, and in 
whom to be unkind is to be harsh or severe. Now 
a conception or term which implies the 
presence of any mark is called Positive, 
as virtue, wisdom, benevolent. A term which im- 
plies the absence of what might belong to a given 
Privative, subject, is Privative, as an unkind or 
Negative. unholy man. Negative terms on the 
other hand, deny not only what does not, but what 
cannot belong to some given object, as lifeless stone, 
speechless block. These do not belong to the clas3 
of Infinitated Conceptions. 

26. These distinctions are not witaout practical 

importance. In the first place they add 

Importance of 

these Distinc- to our variety of forms of thought and 
expression, and so to the means of pre- 
cision of style. The words unkind, unholy, un- 
learned, give us shades of thought not expressed by 



Bee. IX.] CONCEPTIONS. 63 

the words harsh, wicked, ignorant. Again, the 
distinction of Privative and Positive is of moment, 
in reference to the origin of evil as related to God. 
He is in no sense the cause of sin, except privatively 
or negatively. It may arise from the absence, not 
the presence, of his agency, as darkness arises not 
from the presence but the absence of the sun. 

27. Two terms which may be applied to the same 
object at the same time, are called Com- Com?atiHe ^ 
patible or Consistent, as red and round Consistent. 

to a table; diligent and healthy to man. They are 
Opposite or Inconsistent when they can- n . . , 

r r J Opposite and 

not be applied simultaneously to the Inconsistent. 
same object, as " round square figure," " lifeless 
breathing man." 

28. The important distinctions of Abstract and 
Concrete, Connotative and Non-connotative terms, 
were sufficiently explained when treating of the cor- 
responding conceptions. To these the student can 
recur, chap. II., sect. I. 5, and II. 11. 

Sect. IX. — Quality of Conceptions. 

29. By the Quality of Conceptions is meant the 
degree of perfection with which they _ 
represent to the mind the objects and ceptions defined, 



64 LOGIC. [Chap. II. 

the marks included in them. In this regard, Con- 
ceptions, like all cognitions, are perfect in proportion 

When the are aS ^ e y ^ ave ^ e se veral virtues of Clear- 
Perfect. n ess, Distinctness, and Adequacy. In 
proportion as they have the opposite vices, they are 
respectively Obscure, Confused, and Inadequate. 
The nature of these respective virtues and faults we 
will now proceed to explain. 

30. A conception or other cognition is Clear, 

Clear and Oh- w ^ ien ^ * s si m ply distinguishable from 
seme. others, and Obscure when it is not. 

Thus in twilight we often see objects, but are unable 
to distinguish them from each other. Our cogni- 
tions of them are obscure. As the light gradually 
comes upon them, our view becomes so clear that 
we can distinguish them apart. The uninstructed 
cannot distinguish Logic from Psychology and Me- 
taphysics, or a Court of Chancery from a Court of 
Law. These are Obscure conceptions to those un- 
versed in such matters. All persons are afflicted 
with more or less of this obscurity of knowledge in 
departments to which they have not given special 
attention. 

31. But we may know objects or conceptions, so 
as to distinguish them from each other, without 



Sec. IX.] CONCEPTIONS. 65 

being able to point out the marks by which they 

are so distinguished. Such knowledge 

t „ ., -o x -x • Distinct and. 

may be sure as tar as it goes. But it is confused Cog- 
confused with respect to the marks or ^ tiojls ex- 
plained, 
differential features of the object. This is 

among the most common phenomena of our intelli- 
gence. How common to know persons of our acquain- 
tance from each other, without being able to specify 
the peculiarities of form or feature which distin- 
guish them severally. How common to 
be sure as to the hand-writing of differ- 
ent persons, without being able accurately to define 
the peculiarities of each. How often do lawyers in 
court perplex witnesses, and torture out of them 
absurd answers, by asking them the marks by which 
they identify the persons or the hand-writing in 
regard to which they testify. Yet what tribunal 
ever discredited a witness on account of any puzzle 
or inconsistency into which he was thus drawn? 
Those, however, who have made such subjects a 
study, are able to give the marks of difference. 
Their knowledge is distinct, while the other is con- 
fused. The same distinction holds in regard to our 
understanding of conceptions. If we take the con- 
ceptions mineral, plant, animal, man, how few who 

6* E 



66 LOGIC. [Chap. II. 

do not surely know the one from the other ? But 
how few can accurately give the marks which dis- 
tinguish them respectively from each other? A 
Clear cognition or conception then knows its objects 
_. . . B from other objects. An Obscure one 

Distinction of J 

Distinct and does not. A Distinct cognition or con- 
ception not only knows its objects, but 
the marks of those objects. A Confused one knows 
its objects without knowing their marks. 

32. This Distinctness of our conceptions may be 
Adequate and both Adequate and Inadequate. It is 
Inadequate. Adequate when it not only apprehends 
their marks, but the marks of these marks. And 
when it fails of this, it is Inadequate. Thus we 
have a Clear knowledge of the conception man, when 
we discriminate it from animal, plant, etc. We have 
a Distinct knowledge of it, when we know its marks 
to be animality and rationality. This knowledge is 
Adequate when we can give not only these marks 
of manhood, but can also give the marks or defini- 
tions of animality and rationality, those of the former 
being life and sensation, of the latter the intuition 
of supersensual truths and the power of thinking in 
the light of these truths. This process of giving 
the marks of marks is in itself capable of indefinite 



Sec. X] CONCEPTIONS. 67 

3xtension. That measure of it which is adequate, 
cannot be decided by any unvarying No Uiivar . 
rule. It varies with the exigencies and Bales of Ade- 
requirements of each particular discus- 
sion, and must often be determined somewnat arbi- 
trarily. 

Sect. X. — Notative and Symbolical Conceptions. 

33. This is a pregnant distinction. A Nota- 
tive Conception is such that when pre- u otat i Y6 con- 
sented to the niind, it suggests its own ce ption. 
marks (notce) by its very name, so that they are at 
once and indubitably evident, e. g. quadruped, tri- 
angle, octagon, oligarchy. A Symbol- SymDolical 
ical Conception is one which serves as a Conception, 
symbol of a number of marks or characteristics 
which it does not, of itself, bring before the mind 
using it. It is used as a substitute for, or represen- 
tative of, the marks which the mind does not stop 
to bring in detail before itself, and, indeed, which, 
in many cases, it could not, if it would. Such are 
the conceptions or terms, church, family, senate, 
philosophy, etc. Few bring before their minds all 
the marks involved in these conceptions. Most 
persons could not do it, who, nevertheless always 



68 LOGIC. [Chap. II. 

use them with substantial accuracy. All concep- 
tions which are used without an apprehension of 
their marks or definition, are used Symbolically. 

34. All Thorough Knowledge is obtained by re- 
_ moving from our conceptions the several 

Knowledge how imperfections of Obscurity, Confusion 

obtained. 

and Inadequacy, and developing these 
into Clearness, Distinctness, Adequacy and Particu- 
larity ; as also by unfolding the marks of Symbolical 
Conceptions till they have something of the distinct- 
ness of Notative Conceptions. This is no less essen- 
tial to invention and style in Rhetoric, than to 
logical thinking. 

It is accomplished by two great processes, each 
of which must be pursued in proportion as we would 
make our conceptions clear, distinct, and adequate. 

The first of these is Logical Division, which un- 
folds the Extension of Conceptions. 

The second is Definition, which unfolds their In- 
tension. 

These processes are now to be considered. 



Be«. XL] CONCEPTIONS. 69 

Sect. XI. — Logical Division. 

35. Logical Division divides a Genus according 
to its extension, i. e. into its constituent Lo . l D . . . 
and proximate Species. It may then ion Defined. 
take any of these proximate Species for a Genus, and 
divide that into sub-Species. In like manner it may 
divide any of these again, and so on, until we pass 
through Infima Species to individuals. 

36. The Genus divided as being the higher, is 
sometimes called the Super-ordinate. gnper . ordiliate 
The proximate species into which it is Genus. 
divided, are called Co-ordinates. If Co-ordinate 
either of these be divided into parts or s P ecieSi 
Species, with reference to its superior Genus, it is 
called Subordinate Genus. Any one of subordinate 
given Co-ordinate Species, is called, in Genus, 
relation to any one part of a higher or lower Co- 
ordinate Division under the Summum disparate 
Genus, Disparate. Thus, quadruped is Speeies. 
super-ordinate to lions, leopards, horses, Examples, 
cats, etc. They are co-ordinate with 

each other. They are subordinate to quadruped 
and animal, while lion, as compared to fish, Shet 
land pony, or bull-dog, is Disparate. 



70 LOGIC, [Chap. II 

37. The rules for correct Logical Division are : 
a. It must proceed from Proximate Genera to 
Proximate Species, and not per saltum, 
Proximate Ge- or arbitrarily. To Divide animals at 

uera to Pron- once j[ n ^ w hales, sturgeon, etc., without 
mate Species. ... 

previously dividing them into birds, 

fishes, etc., would be a violation of this rule. 

6. There must be but one principle of Division, 
But one Princi- fandamentum divisionis. In dividing a 
pie of Division, library, for example, it will not do to 
divide the books according to price and according 
to binding, at the same time. To do this is to vio- 
late the 

c. Third Rule, which is, that the Divisions must 
Divisions Mntn- ^ e mutually exclusive. They must not 
ally Exclusive. run [ n ^ ^^ other by cross-divisions. 
This will result from adopting more than one prin- 
ciple of Division. Thus if we divide the books of 
a library according to their subject-matter, and ac- 
cording to the language in which they are written, 
some books of poetry, history, and oratory, will be 
in Latin, French, English, etc. One fruitful source 
of perplexity and confusion in the discussion of 
subjects is unobserved cross-divisions, which ought 
rigorously to be avoided. 



Sec. XI.] COXCUPTIOXS. 71 

d. All the parts should be exactly equal to the 
genus divided ; any one part, and the gmn of ^ 
sum of any number of parts less than equals DivisnuL 
all, should be less than the Divisuni or genus 
divided. To divide mankind into rational ani- 
mals and all others, or into Europeans, Asiatics, 
Americans, and Greenlanders, would be a violation 
of this, as well as of other rules. 

e. It must not be a priori, or by Infinitation, 
For this, although in form regular and 
exhaustive, is in fact useless. It adds 

nothing to our knowledge. To divide animals into 
partridges and all others, or partridges and not- 
partridges, is indeed a formally complete, but a 
completely useless Division. Such a Division into 
two members, which inevitably are contradictories, 
is called a Dichotomy. A division in three mem- 
bers is called a Trichotomy : into many members, a 
Polytomy. 

38. Physical Division or Partition. — Logical 
Division must be clearly distinguished from Physi- 
cal Division or Partition. The latter _ ,. ., . 

IndividTials not 

divides an individual, which is logically logically divisi- 

• -■•■•II • • "ble§ 

indivisible, into its component parts, as 

a ship into hull, masts, sails, etc. The test of this 



72 LOGIC. [Chap. II. 

sort of Division is that the Divisum cannot be 
predicated of parts. In Logical Division it always 
may. We cannot predicate ship of sails, masts, 
etc., but we can predicate it of steamship, sailing- 
ship, etc. 

It should be further observed, that we may arbi- 
trarily make collective wholes logical individuals, 
„ „ . when it suits the end in view. Thus 

Collective 

Wholes Logical nations, armies, regiments, etc., may be 
treated as Logical individuals. Often 
like literal individuals they cannot be so divided 
that the divisum can be predicated of the parts. 
Thus army cannot be predicated of regiments, nor 
regiments of companies, nor nations of towns. 

39. The thorough logical division of any subject, 
Uses of Divis- ^hus defining the sphere and the objects 
lon ' it includes greatly assists the clear, tho- 

rough, and facile discussion of it. It also aids in- 
vention. The most sterile mind will find some- 
thing to say on a subject well mapped out. Indeed 
so to map it out, is to say something important. 
Division gives clearness to our Conceptions by 
pointing out their objects. But to gain distinctness 
and adequacy, we must resort to 



8ec. XII.] CONCEPTION'S. 73 

Sect. XII. Defiistction. 
40. This gives the marks of Conceptions, and 
unfolds their Intension, It thus bounds D e fi n i t i 0I1 a e- 
them off from all other Conceptions, so scribed, 
that we not only know that they differ, but in 
what way they differ. The rules for correct defini- 
tion are, 

a. It must be by essential marks. The essential 
marks of a species are what constitute B essential 
its essence, i. e. its genus or matter, and Marks - 
differentia or form. This is normal, logical defini- 
tion, or definition strictly so-called. All other 
definition is valid in proportion as it approximates 
to this. 

Jtgp"* Let not the student forget when asked what is 
logical or essential definition, that it is L ^i ca i D e fini- 
made up of the genus and differentia. tion ' 

b. It must include the objects covered by the 

definitum, or species defined, neither u ot too Broad 

more nor less. If it include more, it is n0T Narrow - 

too broad. Thus to define a whale as a fish, is too 

broad. To define a fish as a whale is too narrow. 

A definition too broad is detected by simple conver- 

Rion. If it is a good definition of a whale to say that 
7 



74 LOGIC. [Chap. IL 

it is a fish, then all fish are whales. A definition 
too narrow is detected by conversion by 
contraposition. Thus, if it be a good 
definition of a fish, that it is a whale, then whatsoever 
is not a whale is not a fish. For the fuller under- 
standing of this, the student must recur to it after 
studying the subject of conversion, in its proper 
place, under the head of Reasoning. 

c. It must not be by Negatives, if this can be 
NotbyNega- avoided. Negatives show what are 
tives. no ^ instead of what are marks, and so 

add little to our knowledge. To define man, as 
not an angel, or not a brute, is unsatisfactory. It 
does not tell what he is. There are, however, Nega- 
tive words and conceptions, which in their very 
nature require a negative definition, as unholy is 
simply not holy. 

d. It must not be in vague, ambiguous, or sense- 
Mast be in clear less language. To say that "truth is 
Language. ^] ie g ran( J scope of all existence," or 
that " beauty is the harmony of being," are exam- 
ples in point. 

e. It must not be Tautological, i. e. through the 

word defined, or any of its derivatives, or 
Not Tautolo- ' J ' 

gical. synonyms from other tongues, or the 



Sec. XII.] CONCEPTIONS. 75 

negative of its opposites. To define life as the vital 
force, or the state of living, or the opposite of death, 
is thus to err. This is definition in a circle, circulus 
in definiendo, for such definitions return upon them- 
selves. If light be defined as " that which illumi- 
nates," per contra, "that which illuminates is light." 
The circle in definition as in argument, is often un- 
observed. How easy to define a plank as a thick 
board, and a board as a thin plank? 

/. It must be Precise and free from surplus 
words. These surplus words, though „ , 

x ' ° Precise and free 

true, may convey a false implication, from Suiplus- 
To say that a parallelogram is a rectili- 
neal four-sided figure, whose opposite sides are 
parallel and equal, is to state the truth. But the 
words "and equal," are unnecessary to the definition : 
and they convey this false implication that there 
may be such figures whose opposite sides are parallel, 
but not equal. This vice is of more frequent occur- 
rence in ordinary thought and speech, than in formal 
definition. How natural to say, " we ought not to 
calumniate so good a man," as if it were right to 
calumniate anybody ? 

41. Absolute Summum Genus cannot be logically 



76 LOGIC. [Chav.il 

defined, because it has no differentia. Thus, being 
can only be defined by some synonym or de- 
scription casually substituted for it. It 
mum Genns not ma y be defined as a thing, or that which 

Logically Defi- } ias existence. Summum Genus in any 
liable. 

particular sphere, being such only rela- 
tively, and always a species of a higher genus, is of 
course capable of strict logical definition. 

42. Simple Ideas are incapable of logical defini- 

Simple ideas ti° n > as ^ e y cann °t be analyzed into 
likewise. elements, and therefore are without 
genus and differentia. They can only be defined 
like Summum Genus, by synonymous or descrip- 
tive equivalents. Red is a color. This is genus. 
But who can give the differentia, that separates it 
from other colors? What is color ? What is good- 
ness or beauty ? What is the respective genus and 
differentia of each ? But although not definable, do 
they need defining ? Are they not self-evident and 
plainer in themselves than any definition could 
make them? 

43. Logical definition, strictly considered, refers 
only to Species, and therefore does not technically 

apply to Individuals. Hence other 

Individuals, 

how Defined. methods of defining them have been de- 



Bee. XII.] CONCEPTIONS. 77 

vised. They may be defined by the intuition of 
them, through the senses if they be bodies, or 
through the light of consciousness, if they be men- 
tal states. Or they may be defined by some pecu- 
liar and inseparable Accidents, as a virtual Differ- 
entia. Thus, Cicero might be defined as " the 
greatest Roman Orator," and the first Napoleon as 
" the greatest French General." They are, however, 
thus defined by all that is essential in a logical defi- 
nition. They are referred to the Infima Species 
under which they fall, and discriminated from other 
individuals under it, by some mark peculiar to them- 
selves. Thus Washington may be defined as " the 
first President of the United States." Here the 
Infima Species, President of the United States, is 
to the individuals under it, what every proximate 
genus is to its co-ordinate species. This then may 
be taken as the genus, and " first" as the dif- 
ferentia. 

44. Indeed, in all definition, whether of indi- 
viduals or species, the genus and differ- a enils m & pif. 
entia may be considered as two com- feren1 ^ a Teall 7 

* two Comnmni- 

municant genera, and the Conception cant Genera, 
defined that which is included within the sphere 

of their coincidence. Either may be considered 

7* 



78 LOGIC. [Chap. II 

genus and the other differentia, and vice versa, at 
convenience, Thus, if we define a man as a rational 
animal, this extends over so much of the concep- 
tions, rational and animal, as overlap each other. 
Thus : 




In like manner, so much of the genera, " Presidents 
of the United States," and " fourth," as overlap 
each other, are just equal to, and define James 
Madison, fourth President of the United States. 

45. As there are many cases in which a strictly 
Methods of De- l°gi ca l definition is either impracticable 
finition, or inconvenient, several other methods 

of defining are occasionally adopted, which serve 
more or less effectually to clear the definitum, and 
to bound it off from all else. Including these, the 
methods of definition in all amount to six, arranged 
oy logicians as follows : 

a. Resolution. This resolves the Conception into 
Resolution, its marks, genus and differentia, and is. 



Sec. XII.] CONCEPTIONS. . 79 

as we have seen, the standard, normal, logical, essen- 
tial definition. Thus, " man is a rational animal." 

b. 'Composition. This is the reverse of resolu- 
tion, and unites the marks into the 
Conception of which they are concrete 

parts. Thus, " a rational animal is man." 

c. Division: i. e. according to extension, into its 
constituent parts, whether species or in- 
dividuals. Thus, "the New England 

States are Maine, New Hampshire, Vermont, Mas- 
sachusetts, Connecticut, and Rhode Island." " The 
animal kingdom consists of Radiates, Mollu^frs, Ar- 
ticulates, and Vertebrates." 

d. By Colligation, the reverse of the last, i. e. 
uniting the constituent parts acccording 

-, T T , Colligatipn.1 

to extension together, as James, John, 
Matthew, Thomas, etc., w T ere the twelve Apostles. 
The Earth, Mars, Mercury, Venus, etc., are the 
Planets. This formula furnishes the minor premise 
for the Inductive Syllogism. 

6. By the substitution of Symbols or Exchange of 
names; as " religion is piety." Symbols. 

/. By Casual Substitution of narrative or de- 
scriptive phrases, as, wisdom leads to 

Casual Snbsti 
virtue and happiness. This last, how- tutioa, 



80 LOGIC. L Chap. IL 

ever, hardly comes up to the exactness required in 
real definition. Nor should the fifth method be 
used when it can be avoided. 

46. Most logicians refer to the distinction be- 
tween Nominal and Real Definition, and strangely 
Nominal and inconsistent accounts have been given 
real Definition, f [^ These terms are adapted to mis- 
lead. Nominal Definition is the Definition of a 
name ; Real, of a thing. But the Definition of a 
name is none the less a Real Definition. Indeed, 
all strictly Logical Definitions are of names, and 
give the marks which these names stand for. That 
id, they give the marks connoted by these names. 
This is the proper, normal province of Definition. 
As to qualities of things not connoted by the name, 
they are important, and belong to scientific investi- 
gation and the increase of our knowledge, but do 
not directly constitute Definition. They may afford 
thf* means of correcting or improving the accepted 
Definition of these names, which is Definition pro- 
per. In Mathematics and the Ideal and Formal 
Sciences, the Definition of the Name, is of necessity 
the Definition of the Thing. The Definition of the 
names, " Circle," " Conception," " Extension/' " In- 



Sec. XII. J CONCEPTIONS. 81 

tension/' etc., is, of course, the Definition of the 
thing. 

47. From this analysis, it appears that Definition, 
or the distinct explication of the marks importance of 
of conceptions, is of fundamental im- Definition. 
portance in thinking, investigating, and discoursing, 
An accurate Definition, or presentation of the status 
questionisy will often settle controversies otherwise 
interminable. Without such Definition, all discus- 
sion and investigation must be futile and unsatis- 
factory. And it is quite as powerful a stimulus to 
invention as Logical Division. 
■48. It is, moreover, quite plain that Definition 
and Division are mutual helps to each 

Definition and 

other. When we Divide a Genus into Division mntnal 
its proximate species, we, of necessity, ^ 
are bringing to light the differences between those 
species. These, with the Genus, make up the Defi- 
nition. On the other hand, looking for the differ- 
ences, we, of course, are finding the boundaries of 
the several species into which Division separates tha 
genus. 

F 



CHAPTER III. 

JUDGMENT. 
Section I. Its Constituent Parts. 

1. Judgment is that act of the mind which, upon 
Judgment de- comparing two Conceptions, or an in- 
fined, dividual object of intuition with a Con- 
ception, affirms that they agree or disagree; that they 
do or do not belong to each other. Thus, "Vic- 
toria is queen." "Angels are not men." A Judg- 
ment expressed in words is a Proposi- 
tion. Judgments and Propositions are 

always either true or false. No other form of 
thought or expression has these attributes. 

2. Strictly speaking, as has been already ob- 

served, in the last analysis, every intel- 
Strictly every 7 J 7 J 

Mental Act a ligent act is a Judgment. To know is 

to discriminate, and therefore to judge. 

Even feeling and sensation, the most rudimental form 

S2 



Sec. L] JUDGMENT. 83 

of consciousness, involves a knowledge and so a 
Judgment that it exists. This is Primitive as 
distinguished from Logical Judgment. PrimitivejTldg . 
And yet it is hard to maintain this dis- menti 
tinction without qualification. For the most Primi- 
tive Judgment affirms that something is p^cates ex- 
or is not; i. e. it affirms that the Concep- istence 01ll y' 
tion, Existence, agrees or disagrees with some sub- 
ject. But beyond the mere predication of Existence, 
Primitive Judgments do not go. Logi- Logical Judg . 
cal Judgments are founded on Concep- ments> 
tions formed by Abstraction and Generalization from 
these Primitive Judgments. Yet, since Primitive 
Judgments involve the Conception of Existence, 
which withal is Summum Genus, the two flow into 
each other. 

3. And it is to be observed, that all the processes 

of Thought, whether by Conceptions, 

5 } / r # ' All Thought 

Judgments, or Reasonings, in reality resolvable into 

ir* i . • t i Judgments! 

proceed from and terminate in Judg- & 
ments. Conception is the product of the Judgments 
involved in abstraction and generalization, whereby 
many objects, through some common mark or point 
of similitude, are grasped together. Conception fixes 
and preserves this Judgment, by a common name. 



34 LOGIC. [Char. HI 

Thus, the conception and the name, bi-ped, is the 
fruit and confirmatory sign of the Judgment, that 
animals, which agree in having two feet, may be put 
in a class denoted by the common name, biped. As 
Conception is the product of a Judg- 
formedandex- ment > so Jt is explicated by a Judg- 
piicatedby ment# Thus " bi-peds are two-footed 

Judgments. 

animals." " Animals are conscious." 
They interpen- j n short, Conception and Judgment in- 

etrate each 

other. terpenetrate each other. In one view, 

Conception is a certain stage of Judg- 
ment. Judgment in form develops Conception. 
Reasoning, too, the third great process 

Reasoning also . 

is by Jndg- or form of thought, deals only with 
Judgments, and their relations to each 

other, as will be seen, when we come to treat of it. 

It proceeds from one or more Judgments given to 

others founded upon them. Thus, in the last 
analysis, Logic being the Science of 

Logic the Sci- 
ence of Judg- Thought is the Science of Judgments, 

ments. ^ Q w j 1 j c j 1 a n thought is finally resol- 

vable. Nevertheless it is convenient to treat of 
pure formal Judgment by itself, after Conception 
which furnishes the materials of Judgments ; and 
before Reasoning, which is composed of them, and 



Sec. L] JUDGMENT 85 

in concluding that one Judgment flows from others, 
form? the Judgment that it does so. 

4. Judgment being thus a mental affirmation of 
the agreement or disagreement of two notions, one 
of which at least is a Conception, Terms of a 
these two notions are called the terms Jlld g ment ' 
(termini, extremes) of the Judgment. 

That which is spoken of is the Subject of the 
Judgment. That which is affirmed or g^j ectj p re aj.. 
denied of the other is called the Predi- cate ' 
cate. That which connects the two is 

Copula is verb 

the Copula. This is always the verb "to be "in pres- 
to be, in the Present Tense Indicative, 
if the Judgment be affirmative : and the same with 
the negative particle affixed, if the Judgment be 
negative. Thus : 

Sub. Cop. Pred. 

The earth is round. 

Sub. Cop. Pred. 



Oaks are not pines. 

The Copula, in many cases, is not directly ex 
pressed by the word is, or is not, but is o P nlaofteninv 
in other phrase, which implies them. P 11 ^ 
When any other than the Substantive verb is em- 
ployed as Predicate it includes the Copula. Thus, 

3 



86 LOGIC. LChap. Ill, 

Sub. Cop. Pred. 

"he runs," is equivalent to, he is running. " No men 

Sub. 

are sinless/' is the same as to say of |all men| that 

Cop. Pred. 

they |are not| sinless. 

When Existence simply is expressed, the verb 
Predicate when to be is both Predicate and Copula; as, 

, _ Sub. Pred. Cop. 

m * h ^ God is = is existing. 

5. When any mood or tense of the verb, except 

the present indicative in the Copula, is 

to the Predi- significant, this significance belongs to 

the Predicate and not to the Copula. 

Thus, if we say, " This farm was fertile, whether it 

be so now or not," it is the same as to say, this farm 

Pred. 



is I one formerly fertile! . The weather may be good, 

Pred. 

the weather is (what may be good I. As either term 
of a Judgment may be a Conception including differ- 
ent objects, or having several marks, so several words 
may be employed to make up a term. Thus, |" The 

Sub. Cop. Pred. 

dews of the evening! are [the tears of the sky."] 

" Birds, fishes, beasts, and reptiles, are animals." 

6. Words which alone cannot express conceptions, 

Categorematic or intuitions, cannot of themselves con- 
ana riyncatego- , 
rematic Words, statute terms of a Judgment. They can 



Bee III.] JUDGMENT. 87 

only enter into these terms by combination with 
verbs and nouns substantive and adjective. Such 
are articles, prepositions, conjunctions and adverbs. 
These are Syncategorematic ; nouns, adjectives, and 
verbs, on the other hand, are Categorematic, because 
they can of themselves be Terms. 

Sect. II. — Quantity, Quality, Eelation, and Modality 
of Judgments. 

7. Judgments may be viewed, I. 

Judgments in 

With reference to the relation of the respect of Quan- 
predicate to the extension of the sub- ^ iJt 
ject — Quantity. 

II. With respect to the relation of the predi- 
cate to the intension of the subject — 
Quality. «-"* 

III. With respect to the manner of connecting the 
predicate with the subject — Relation. Kelation. 

IV. With respect to the degree and kind of cer- 
tainty in the connection of subject and 
predicate — Modality. 

Sect. III. — Quantity of Judgments. 

8. With respect to Quantity, Judgments are either 

Universal, Particular, or Singular. 

7 & Universal 

Judgments are Universal when the Pre- Judgments. 



88 LOGIC. [Chap. III. 

dicate is affirmed or denied of all the Subject taken 
distributively, as, " all men are sinners f " no men 
are angels." 

Judgments are Particular when the Predicate is 
affirmed or denied of an indefinite part of the sub- 
ject, as, "some men are orators;" "some 
Governments are not Democratic." 
Judgments are Singular ; a. when the Predicate 
is affirmed or denied of individuals, as, 
"Csesar was a Conqueror;" "this man 
is not learned." b. When the subject is a plurality 
of individuals taken collectively. A collective noun 
is, for Logical purposes, Singular: as, "This crowd 
is tumultuous," " An army consists of soldiers." 
9. Singular Judgments, for all Logical purposes, 
may be accounted as Universals, since 
mTnt^'eqniva- in them > the whole subject is spoken of, 

lent to Univer- an( J fo^y are subject to the laws of 

sals. 

Universals. 
In like manner, when any Definite part of the 
Subject is taken, it may be considered 

Also a Definite J ; V 

part of the Sab- as a universal. For the whole class 
]ectl denoted by the subject-name with its 

limiting adjuncts is spoken of— Thus " these men are 
natives of Ireland." 



Sec. IV.] JUD GMENT. 89 

It is in place here to add, that Judgnienls are 
further distinguished as Simple and Compound. 
Judgments are Simple when, in fact as well as form, 
there is but one subject and one Predicate, as, u men 
are rational animals." A Judgment is m \ 

c Simple and 

Compound when, though simple in form, Compound 
by a plurality of subjects or predicates, 
there is in force and effect a plurality of Judgments. 
Thus, " Peter, James, and Thomas were Apostles," 
amounts to three propositions, one affirming of Peter, 
another of James, and another of John, that he was 
an Apostle. "Men are rational, accountable and im- 
mortal," may be divided into three propositions, each 
having "men" for the subject, but one having the 
predicate " rational," the other " accountable," etc. 

Sect. IV. — Quality of Judgments. 
10. The differential Quality of a Judgment is 
that it affirms or denies the agreement of 

Quality respects 

Subject and Predicate. Hence in respect Affirmation or 
of Quality, Judgments are either Affir- ega lon * 
mative or Negative, ggg 3 * Let the learner remember 
that the Logical Quality of a Judgment refers to its 
being Affirmative or Negative. The truth or falsity 
of a Judgment is of course of supreme importance. 

8* 



90 LOGIC. [Cha IIL 

But this pertains to its matter, not to its form, with 
which alone formal Logic concerns itself. 

11. A Proposition is Affirmative or Negative, ac- 
cording as it has not or has, a negative Copula; 
Quality in the *■ e * when, whatever be the form of ex- 
Copnla. pression, the real force of a negative 

does not or does, fall on the Copula. Thus, " no 
iron is silver/' is negative, for it asserts 
of all iron that it is not silver. " A per- 
son not vicious is virtuous," is affirmative, because 
the force of the negative does not fall on th** Copula 
but on one of the terms. "A few men are> ndse r " is 
affirmative ; " but few men are wise," is in ^ality ne- 
gative, for it is equivalent to " most men arr not wise." 

Judgments then as to Quantity and Quality, as 
The four Logi- thus unfolded by the old Logicians, 

cal Judgments r> r • r ,i i i 

and their Sym- are f ° Ur > whlch the y have been accu ^ 

bote tomed to mark by the Symbols, A. R 

I O., as follows : 

Universal Affirmative, .... A. 

Universal Negative, E. 

Particular Affirmative, .... I. 
Particular Negative, .... O.* 

* The additional Judgments recognized by recent L.'giciani 
will be noticed in due time. 



8ec. VI.] JUDGMENT, 91 

Sect. V. — Distribution of Terms in Judgments. 

12. Of the foregoing Judgments all Universals 
and no Particulars distribute the Subject. 

All Negatives and no Affirmatives tr ™theSub" 
distribute the Predicate. J ect - Natives 

the Predicate. 

The reason of the first rule is obvious, 
for in Universals the whole subject is spoken of 
Distributively.* In Particulars only a part of it. 

No Negative Judgment can hold good unless it 
cuts off the whole of the Predicate from the subject. 
Thus, if we say, " some men are not poets," the 
whole of the class of poets is cut off from these "some 
men." " No men are perfect," cuts off the whole of 
the class "perfect" from the class men. 

Sect. VI. — Kelation of Judgments. 

13. The Relation of Judgments has respect to the 
manner of the connection between the „ , . 

Relation either 

subject and Predicate. In this respect Categorical o* 
Judgments are either Categorical or ypo 
Hypothetical. 

* Collective Nouns are no real Exception, since in a Logical 
sense, they are individuals and form the subjects of Singular 
Judgments. 



92 LOGIC. |Chap. HL 

14. A Categorical Judgment asserts or denies the 

agreement between the subject and Pre- 
dicate, simply and unconditionally, as, 
u Brutus killed Caesar," " a traitor is not a patriot." 

15. A Hypothetical Judgment asserts or denies 

such agreement upon a condition, viz : 
of the truth or falsity of some other 
Judgment. Thus, "if crops are large, food is 
cheap." " This man is either holy or unholy." 
T , , . , f 16. Hypothetical Judgments are of 
Hypothetical three kinds : Conditional, Disjunctive, 

Judgments. -i t^m 

and JJilemmatic. 

17. The Conditional Judgment affirms such a 
Conditional elation between two others, respec- 
Jndgments. tively called Antecedent and Conse- 

Antecedent and <l u ent, that > if the former be true, the 
Consequent. l atter j s true a \ S0) as ^ « jf t h e sun 

shines, it will give heat." Conditionals are indi- 
cated by the particles, "if," or its equivalents, 
" when," " in case of," etc. 

18. The conditional, like all hypothetical, has 
„ , . in it a categorical element, i. e. it asserts 

Hypotneticals ° 

baveaCategori- categorically a certain relation between 

the Antecedent and Consequent; such, 

that, if the former is true, the latter is true ; and if 



Sec. VI.] JUDGMENT. 93 

the latter is false the former is false. It often ex- 
presses the relation of cause and effect. M , „ , , 

* Causal Relation 

If the cause operates the effect will fol- often in Condi- 
low. It is to be observed that a condi- 
tional does not assert the truth of either of its mem- 
bers, but of the relation between them. 

Do not assert 

It may assert, not only a causal rela- the truth of 

*• u a xi> x j.1. j? j. • either member, 

tion, but the truth ot a certain argu- 
ment. Thus, " if drunkards drink what intoxicates, 

A. B. drinks what intoxicates." This 

. . ,i,i i Other relations. 

is not an assertion either that drunk- 
ards, or A. B. drink what intoxicates ; nor that the 
former is the cause of the latter ; but that there is 
such a relation between the two, that if the former 
be true the latter is true. A certain fact, however, 
is by implication asserted as the foundation of this 
relation, viz., that A. B. is a drunkard. 

19. Disjunctive Judgments assert the connection 
between the predicate and the subject, „, , 

x v ? Disjunctives as 

with an alternative indicated by the sert with an al- 
particles, either and or. Thus, "it is 
either Spring, Summer, Autumn, or Winter." The 
force of it is that if one member be affirmed, all the 
others are denied. If one is denied, then some one 
of the residue is true. This is founded on the law 



94 LOGIC. [Chap. Ill 

of Excluded Middle. A judgment or its contra- 
Founded on Ex- Victory must be true, and there is no 
eluded Middle, middle between them. So conditionals 
are founded on the law of Sufficient 

Its members 

mutually exclu- Reason. Of categoricals the affirma- 
tives are founded on the principle of 
Identity, and the negatives on the law of Contradic- 
tion. 

20. Hence, in order to any valid conclusion from 
the affirmation or denial of either member of a dis- 
junction, these members must be mutually exclusive. 
Indeed such alone are genuine disjunctives. Dis- 
Differ from Par- junctives must not be confounded with 
titives, Partitive Judgments, which, under the 

form of a disjunctive, simply predicate of a genus 
its several species ; as, "all Africans are either bond 
or free." This is but dividing the genus into its 
component parts or species. It differs from the dis- 
junctive in this, that the predicates are affirmed 
concurrently, and not alternatively, of the subject. 
The affirmation of the one is not, as in a pure dis- 
junctive, a denial of the other, although the predi- 
cates are still mutually exclusive with regard to the 
portions of the subject to which they respectively 
belong. 



Sec VII.] JUDGMENT. 95 

21. Dilemmatic Judgments involve a combina- 
tion of the conditional and disjunctive. Dilemmatic 
Thus, " if A. B. succeeds, he will either Judgments. 
rule or ruin." Here the disjunction is in the conse- 
quent of the conditional. It may also be in the 
antecedent. " If man is either good or ill deserving. 
he is a moral agent." 



Sect. VII. — Substitutive Judgments. 
22. Substitutive Judgments are those which being 
affirmative have a distributed predicate, g^stitutivea 
This distribution of the predicate can- defined. 
not be known from the mere form of expression. 
As we have already seen, affirmatives as such, do 
not distribute the predicate. To say that men are 
mortals, is merely saying that they are in the class 
of mortals. They in fact comprise a 
part but not the whole of mortals. But 
if we say, u men are rational animals," we mean all 
rational animals, for there are none but men. This, 
however, does not appear from the affirmative form 
of expression, any more than, if we were to say, 
" men are animals." We know it from other evi- 
dence. "Rational animals" is the definition of 



96 LOGIC. [Chap. IIL 

men, and is, therefore, co-extensive with it. In all 
All Definition cases of Definition then, and in all the 
Substitutive. kinds of Definition which have been 
pointed out, we have Substitutive Judgments. 

23. Judgments of this kind are called Substitu- 
Why called ^ ve > because the predicate may be sub- 
Substitutive. stituted for the subject without limiting 
the quantity, either of the judgment, or of the predicate 
substituted. If we define men to be rational ani- 
mals, we can say that u all rational animals are 
men." If we say that " Maine, New Hampshire, 
etc., are the New England States," we can, by sim- 
ple substitution, say that u the New England States 
are Maine, New Hampshire, etc." 

24. Substitutive Judgments are either Particular 
„. , ^ . or Universal. Of these latter we have 

Either Particu- 
lar or Univer- already given examples. The former 

are such as, "some stars are planets," L e. 

all the planets: "some men are poets," i. e. all poets. 

25. Affirmative Judgments, in which the predi- 
Attributive ca ^ e * s undistributed, are called Attri- 
Jndgments. butive, because they affirm an attribute 
of the subject, without taking this attribute in its 
whole extent, or substantively. Thus, " men are 
rational." 



Sec. VII.] JUDGMENT. 97 

26. The importance of Substitutive Judgments 
will appear, when we come to treat of 

Importance of 

the subject of reasoning. They render Substitutive 
many processes of reasoning valid, ^S 1116111 ^ 
which would otherwise be invalid, owing to the non- 
distribution of affirmative predicates, as will be ex- 
plained in the proper place. 

27. The reason why logicians who have recog- 
nized this class of judgments, have Why this per- 
treated this subject as belonging to the * a * ns t0 . t T e /q re " 

J © © lation of Judg- 

Relation of judgments, or as concerned ments, 
with a peculiar class of them, in respect to the man- 
ner of the connection of the subject and predicate, 
is, that it exhibits the quantity of the predicate as 
related to the subject. Indeed every affirmative 
judgment, w T hen fully explicated in language, be- 
comes an equation of the subject and predicate as to 
quantity, and so a Substitutive Judgment. This 
will appear if we explicitly quantify EqTiationofSnl) . 
the predicate, i. e. fully express in words ject and Predi- 
what we mean in thought. Thus, if 
we say, " all men are mortals," we mean, " they 
are (i. e. =) some mortals." " All men are rational 
animals," means " all men are (i. e. =) all rational 
animals." 



98 LOGIC. [Chap. Ill, 

28. Substitutive Judgments are indicated respec- 
tively, the universals by the letter U, and the par- 
ticulars by the letter Y. Thus, we have 

The Symbols # J ' 

of Substitutive six different kinds of judgments, desig- 
nated by their several symbols as 
follows : 



Universal Attributive, .... A. 
Particular Attributive, .... I. 
Universal Negative, . . . . E. 
Particular Negative, . . . . O. 
Universal Substitutive, . . . U. 
Particular Substitutive, . . . Y. 

29. [Besides these, Sir William Hamilton has 

._ ^ >x _ undertaken to develop two others ; viz., 

Negatives with r * 7 

undistributed Universal and Particular Negative 
Judgments with undistributed predi- 
cates, which he marks by the respective symbols fj 
and co. But undistributed negative predicates are 
so contrary to all normal thought and language, 
that, at best, they are useless, and need not claim 
our attention. The Judgments, " No men are some 
animals," " and some men are not some 

Insignificant 

and worthless, animals," are awkward, insignificant, 



Bee. VIII.] JUDGMENT. 99 

and worthless, being nearly, if not quite incapable 
of real contradiction.*] 

Sect. VIII. — Analytic and Synthetic Judgments. 

30. Analytic Judgments are those in which the 
predicate is involved in the very Con- 4^^ j u & gm 
ception or Definition of the subject. As, meilts ' 
" man is rational." " Quadrupeds are four-footed." 

* They cannot, with slight exception, be opposed by contrary 
or contradictory propositions, in any normal use of language. 

The following table in which A stands for a distributed, and I 
for an undistributed term, and the letters f and n respectively 
for an affirmative or negative copula, exhibits at a glance the 
import and force of the Eight Judgments recognized by Hamilton. 

A. Afi. All are some. All men are mortals. 

E. Ana. Not any is any. No men are angels. 

I. In. Some are some. Some trees are beautiful. 

0. Ina. Some are not any. Some coins are not silvei. 

U. Afa. All are all. All men are all rational animals. 

Y. If a. Some are all. Some men are all the poets. 

»7. Ani. Not any are some. No planets are some stars. 

<•>. Ini. Some are not some. Some trees are not some oats. 

6) is without force because not contradictory to nor inconsistent 
with any other proposition, rj may indeed have greater force. But 
this is seldom important in actual thought. Both judgments in- 
deed z.re rather conceivable than actual in normal thought, and 
for practical purposes, without assertory force. 



100 LOGIC. [Chap. Ill 

They therefore require no proof. They are evident 
simply from the analysis of the subject. Hence 
they are a priori, i. e. known from the conditions 
given, if not always in the most absolute meaning 
of a priori, yet from the definition of the subject, 

31. Synthetic Judgments are those in which the 
Synthetic Judg- predicate adds to the conception or defi- 
ments. nition of the subject. They, therefore, 

require proof. Thus: " laurel- water is poisonous," 
"horned animals are ruminant," "the conception 
of a perfect being involves his existence." Synthetic 
Judgments are, with a qualification to 
■p ..." be noted, a posteriori. The Formal 

Lxception in 7 jr 

Formal Sci- Sciences, and those which deal with 

ences. 

necessary truth, furnish us a peculiar 

class of Judgments that are both synthetic and a 

priori All the demonstrated proposi- 

. How tney give A x x 

SyntheticJudg- tions in Geometry, e. g. are a priori. 
Yet they are not a part of the definition. 
They are not immediately suggested or implied by 
it. They require to be proved by a chain of reason- 
ing from the definitions, more or less extended. 
Yet this reasoning is a priori. The same is true of 
most of the principles of Logic. In this sense we have 
Synthetic Judgments a priori. They are, in truth 



Sec.. IX. J JUDGMENT. 101 

partly analytic, in that they are ultimately evolved 
from the definitions ; synthetic in that they require 
proof beyond the mere statement of the definition. 
The origin of this use of the terms analytic (avakoo), 
to take asunder), and synthetic (aovridrjfii, to put 
together), is evident from their etymology. 

The terms Explicative and Ampliative have, for 
obvious reasons, been employed to de- Explicative ^ 
note the same properties of Judgments Ampliative. 
as Analytic and Synthetic. 

Sect. IX. — The Modality of Judgments. 

32. The Modality of Judgments respects the pos- 
sibility, certainty, or necessity of the The Modality of 
connection of the predicate with the J^J^ 
subject. This, however, really belongs L °g iCi 
to the meaning of the predicate rather than to the 
copula, or any part of the logical form of the judg- 
ment. Strictly, therefore, it pertains to the matter 
rather than the form of the judgment, to Metaphy- 
sics instead of Logic. It belongs, accordingly, 
rather to applied than to pure Logic. To this we 
shall therefore defer it, although it is sometimes 
treated at this point. 



9* 



102 LOGIC. [Chap. Ill, 

Sect. X. — Plurative Judgments. 

33. Plurative Judgments are those in which 
Plurative Judg- more than half, but not all of the sub- 
ments defined. j ec ^ j s taken j as, " Most men are vain." 
Of a similar nature are Numerically Definite Judg- 
„ , „ ments, i. e. those in which a definite 

Numerically r 

Definite Judg- number or numerical proportion of the 

ments. i . > • . i 

subject is taken. 
Both of the foregoing have some importance as 
giving rise to a peculiar kind of valid syllogism 
which will be explained in its proper place. See 
chap. V. ? sect. I. 5. 

Sect. XI. — Conversion of Hypotheticals into Catego- 
ricals. 

34. It has already been shown that in every 
„ A A . , Hypothetical Judgment there is a cate- 

Hypotneticals ^ L ° 

have a Oate- gorical element, which affirms or de- 

gorical element. . , . , , . , 1 . , 

nies the given hypothetical relation be- 
tween certain categorical judgments. This being so, 
by a slight change of phrase, they may be made 
Categorical in form. This can be done, as follows, 
a. Conditionals may be so converted by substi- 
Conditionals tuting for the particles " if," " when," 

how turned into t ' ? 

Oategoricals. etc., which have a conditional force, 



Sec. XL] JUDGMENT, 103 

such phrases as "the case of/ 7 tiie "circumstances 
in which/ 7 etc. Thus the conditional, if A is B, 
X is Y, is the equivalent of, " the case of A be- 
ing B is the case of X being Y," which is a 
categorical. The conditional, " if the thermometer 
is at zero, ice forms rapidly/ 7 may be transformed 
into, " the case of the thermometer being at zero/ 1 
or ;% the case/ 7 or "the circumstance/ 7 or "the 
time in which the thermometer is at zero, is that in 
which ice forms rapidly." 

Certain Abbreyiations are practicable when the 
same terms are found in both antece- 
dent and consequent. Thus the condi- ^ tlie case 
tional, "if Peter is a drunkard, he of onl y three 

Termsi 

(Peter) is degraded/ 7 is equivalent to 

" every drunkard is degraded/' otherwise it could 

not be true. 

b. Disjunctives may be turned into Categoricals 
by using all their members for one of 
the terms, and the phrase, "possible ls ^ Tm<il 
cases/ 7 or the like, for the other, thus forming a 
judgment by Colligation, which, as we 
have seen, is the opposite of Logical * ^ lg& 0A * 
Division. Thus: "This season is eitW SVnng, 



104 LOGIC. [Chap. III. 

Summer, Autumn, or Winter," is equivalent to 
either of the eategoricals, "the possible cases in 
regard to this season," or " the only alternatives in 
regard to it, are Spring, Summer, Autumn, Win- 
ter." 

As has been shown before also, Disjunctives may 
D „ , , . be turned into Conditionals, by taking 

Bj first being 7 J ° 

turned into Con- the contradictory of one of their mem- 
bers for the antecedent, to which the 
other members become consequents. Thus, in the 
foregoing example, " if it is not Spring, it is either 
Summer," etc. When once a conditional, it can be 
made a categorical, according to the rules already 
given, e. g. " The case of its not being Spring, is 
the case," etc. 

c. Dilemmatic Judgments being compounded of 
Conditionals and Disjunctives, may be 

Dilemmatic J 7 J 

Judgments to be resolved into these, and each of these 

Resolved, , .. , . , 

may be changed into categoncals, ac- 
cording to the methods just indicated. Thus, the 
Dilemmatic Judgment, " If iEschines did or did 
not join in the public rejoicings, he was either in- 
consistent or unpatriotic," may be analyzed ; "If 
he joined, etc., he was inconsistent;" "If he did 



Sec. XL] JUD GMEXT. 1 05 

not join, etc., he was unpatriotic;" "But he did 01 
did not join ;" " He was either inconsistent or un- 
patriotic." These may be turned into Categoricals 
by the methods already prescribed. 



CHAPTER IV. 

RfcAfeUJTCNG — IMMEDIATE INFERENCE. 
Section I. — Introductory Remarks. 

1. The next stage of Thought after the forma- 
fceasonmg De- ^ on of Judgments, is that of deriving 
fined. from judgments given other judgments 
founded upon them. This is Reasoning. 

2. Reasoning is by inference from one Judgment 
mr 3 , JT to another derived from it; or from two 

Mediate and Im- ' 

mediate Infer- judgments to a third, which could not 

be derived from either alone, but flows 
from both combined. The former is called Reasoning 
by Immediate Inference, the latter by Mediate In- 
ference, L e. from one judgment through the medium 
of another ; or more strictly, as it will more fully 
appear, through a middle term, medius terminus, 
wmmon to both the judgments given, by means of 
i common or opposite relation to which, the two 

106 



See. II.] IMMEDIATE INFERENCE. 10/ 

terms of the conclusion are found to agree or disa- 
gree with each other. These two kinds of reasoning 
will be severally treated in their order. 

3. Immediate Inference, L e. infer- Three kinds of 
ence of one judgment from another, is J 11111 * 

J & ; ference. 

of three kinds, termed Opposition, Opposition, Con- 
Conversion, and Equipollence or Infi- verslcm > E( l u> 

x * pollence or Infi- 

nitation. And first of, nitation. 

Sect. II. — Opposition. 

4. Opposition exists between judgments having 
the same subject and predicate, but dif- opposition de- 
fering in quantity, or quality, or both. finedi 
Thus, " all A is B," and "some A is not B," are op- 
posed. They differ both in quantity and quality. 
This is the strongest kind of opposition, called con- 
tradictory. From any judgment whatever, an infer- 
ence can be made regarding its contra- 

,. . , . , . ,, ., . Contradictories. 

dictory, or which is the same thing, any 

affirmation or denial regarding either of two con- 
tradictories, warrants an inference in regard to the 
other. Thus, if we take the two contradictoi ies, 
" all men are mortal/' " some men are not mortal/' 
when either is true the other is false; when either is 
false the other is true. 



108 



log- i a 



[Chap. IV. 



5. Besides the Contradictories, we have the Con- 
traries A and E, and the Sub-Con* 

Contraries, ' 

Bub-Contraries, traries I and O, which respectively dif- 
fer in quality alone. Also the Subal- 
terns. A and I, E and O, in which the members 
of each respective pair differ from each other only 
in quantity. In each pair of these the Universal is 
SaMternans. called the Subalternans, the Particular 
Snbaltemate. the Subalternate. All these forms of op- 
position are brought compactly and clearly to view 
by rtie following ingenious and simple diagram, 
wbHh has been devised by logicians. 



Contraries. 




Sub-contraries 



Bee. II.] IMMEDIATE INFERENCE. 109 

6. The Laws of Inference in the case of judg- 
ments in opposition are ; in brief, as fol- Laws of Infer- 

, ence in Opposi- 

lows : tion. 

a. Of Contradictories one or the other must be 
true, both cannot be true. And by the Ee -Contradicto 
law of Excluded Middle no interna e- ries> 
diate between them can be true. Therefore, from 
the truth of either of two contradictories, it follows 
that its opposite is false ; and from the falsity of 
either, the truth of the opposite may be inferred. 

6. From the truth of either Subalternans, the 
truth of its Subalternate follows. From 
its falsity nothing follows with regard 
to the Subalternate; from the truth of either Subal- 
ternate nothing follows in regard to its Subalter- 
nans. From the falsity of the Subalternate the 
falsity of the Subalternans results. 

c. From the truth of a Contrary the falsity 
of the opposite Contrary follows. But 

from the falsity of one Contrary, nothing 
follows in regard to the other. 

d. From the truth of either Sub-Contrary nothing 
follows in regard to the other Sub-Con- 

■n , * ^ ,. n, n Sub-Contraries. 

trary. But from the negative of one of 

them, it follows that the other must be true. 

10 



110 LOGIC. [Chap. IV. 

7. From this it appears that the Opposition be- 

tween Contradictories is far the most im- 

Contradictory 

Opposition most portant and fruitful of inferences. The 

mportanti n ui j x» • ±.\ 

* most available mode of proving the 

truth of many propositions, is to prove their Con- 
tradictories false. 

8. The foregoing view exhausts opposition as 

between the four fundamental judg- 

Other forms of . ^ T , ^ , , 

Opposition crea- ments A E I and O above recognized 
tedbytheJndg- ^y t h e \^ logicians. But if we bring 

ments UandY. / # & m rt 

in the additional substitutive judgments 
U and Y already considered, they lay a founda- 
tion for other forms of Opposition. 

a. For other forms of Contrary Opposition. The 

characteristic of this kind of opposition 

Other forms of x x 

Contrary Oppo- is, that of two judgments opposite in 
quality whatever their quantity, both 
judgments may be false, but cannot be true together. 
Thus A and E may both be false, but cannot both 
be true together. But the same is true of E and U. 
Thus, it is false alike that " no men are poets/' and 
that " all men are all the poets." It is true that 
" all men are all rational animals," false that " no 
men are rational animals." 

b. Out of the Opposition of these Substitutive 



Sec. II.] IMMEDIA TE INFERENCE. Ill 

Judgments to each other, and to other judgments 
arises what has been named Inconsistent iaco^isteiit 
Opposition. This obtains bet ween judg- Opp° sition - 
ments opposed in quantity but not in quality, which 
cannot both be true, though both may be false, at the 
same time. Thus the opposed judgments A and U 
cannot both be true of the same subject and predi- 
cate, unless A be considered, as it was by old logi- 
cians, to include U. It cannot be true that all men 
are all the animals (U), and that all men are only 
some animals (A). But A and U may both be 
false, as in any subject and predicate in which ne- 
gatives or particulars only are true. 

c. Subaltern Opposition exists when there is more 
distribution in either term of one judg- New Bnbaltern 
ment (the Subalternans) than in the Opposition. 
corresponding term of the other (the Subalternate). 
Accordingly, this kind of opposition exists between 
U and I, also between Y and I, for from positing 
either U or Y, I may be inferred. But from I 
neither U nor Y can be inferred. 

9. Applying these principles, and extending the 
diagram of Opposition already given to include U 
and Y, we have the following result : 



112 LOGIC. [Chap. IV. 
U Inconsistent A Contrary E Contrary ; U 



i " s «>. .J^ % '"'°o. ,^ W "''On 



5^\ I >>X I ^ 






Y. # ...... Subaltern .*.i*«.. Sub-contrary..!'. 6*... Sub-contrary... Y* 

10. Opposite Judgments must have the same 
subject and predicate, not only in sound but in 
sense. " Bread is heavy," and " bread is not heavy," 
are not opposed, if in the former case "heavy" be 
used to denote imperfect fermentation, in the latter 
to denote specific gravity as compared with lead. 

* Some writers, among whom is Thomson in his Laws of 
Thought, class the opposition between A and 0, as Contrary in- 
stead of Contradictory, and admit only E and I to be Contradic- 
tories. He says, " We cannot tell from the removal of whether 
we ought to replace it by A or U." This, however, though theo- 
retically true, hardly calls for a deviation from the established 
use of terms in practice. Would not this argument abolish the 
contradiction between E and I? If E be removed, we do not, 
from that fact, know whether it may not be replaced by A, U, or 
Y, as well as I. We only know that as much as I is true. In 
like manner we know that certainly as much as A, and possibly 
as much as U, is true if be removed. This gives them both the 
power of contradictories. How much more is true in any case 
must be learned from other sources. Y is a kind of false sub* 
contrary to 0. If it be true, is true. 



Sec. III.] IMMEDIATE INFERENCE. U3 

Sect. III. — Conversion. 

11. A second mode of immediate inference is by 
Conversion. Propositions or judgments Conversioil De . 
are converted when the predicate and finedi 

the subject change places, in such a way that the 
converse is an inference from the convertend or 
judgment converted. 

12. In order that Conversion may be illative, or 
give rise to a legitimate inference, no Law of Distri . 
term must be distributed in the con- tation of Terms. 
verse which was not distributed in the convertend: 
otherwise more would be spoken of in the conclu- 
sion than in the premise. This was the rule of the 
older logicians. 

13. Hamilton and his school, however, maintain, 
not only that no term should be distri- Hamilton's 
buted in the converse which was undis- LaWi 
tributed in the convertend, but that all terms dis- 
tributed in the latter should be distributed in the 
former. 

14. Conversion, in order to be logical, according 
lO these principles, sometimes requires 

a change in the Quality or Quantity of tii^TSj" 
the convertend. Hence result the fol- som etimes n<n 

cessary. 

lowing modes of Conversion. 
10* H 



114 LOGIC. [Chap. IV. 

A. Simple Conversion is when there is no 
Simple Conver- change in either Quality or Quan- 
8ion « tity. 

B. Conversion by Limitation, sometimes called 
By Limitation P er aacideins, is when the quantity is 
or per accidens. changed from universal to particular. 

C. When the quality is changed, it is said 
Negation and to be by Negation or Contra-posi~ 

flontra-position, ±* 

15. Accordingly, 

a. A, which distributes the subject but not the 
How to Convert predicate, must be converted by Limi- 
Ai tation from universal to particular, and 

therefore, according to the old Logic, which does 
By old Logic A. no * reco g n i ze the distribution of affir- 
becomes I. mative predicates, becomes I ; but with 
a quantified and distributed predicate it becomes 
Y. Thus, "all men are mortal," becomes in the 
former method, "some mortals are men," which is I; 
and in the latter method, "some mortals are all men," 

In perfect Con- which is Y - l4 is J ustl y argued that 

version A. be- the latter is the only perfect Conversion, 
comes T. . 

because it alone enables us, by recon- 
version to regain the original convertend. This 
ought to be possible in thorough conversion. From 



Sec. III.] IMMEDIATE INFERENCE. H5 

" some mortals are men," i. e. " some men," we can 
only get by re-conversion, " some men are mortals." 
But from " some mortals are all men," we readily 
get back the original convertend, "all men are 
mortals." Of course from Y comes I, 

., •• -i. . Y involves I. 

its subalternate. 

6. E., which distributes both terms, may be 

converted simply, and remains E after E converted 

conversion. If, " no men are angels," ^P 1 ^ 

then " no angels are men." 

c. In like manner I, which distributes neither 
term, may be converted simply. If 

some Americans are Indians, then some 
Indians are Americans. 

d. O distributes the predicate but not the subject. 
Consequently, if it were converted with- ^ 

1 * ' converted oy 

out changing its quality, the subject un- contraposition 

distributed in the convertend, would be an w y ' 
distributed in the converse by being the predicate 
of a negative. Thus, " some quadrupeds are not 
horses," would become u some horses are not quad- 
rupeds," which i« obviously illogical as well a& 
false. 

In order to avoid this, the negative particle is 
transferred from the copula to the predicate, so that 



116 LOGIC. [Chap. IV, 

the convertend becomes I, which may be simply con- 
verted. Thus, for "some quadrupeds are not 

Pred. 

horses/' say, " some quadrupeds are |not horses|," or 
" things not horses/' This is I, which converted 
simply becomes, "some things not horses are quad- 
rupeds." Here conversion is by contraposition. 

16. A and U, L e. all affirmatives which have 
Conversion of A the subject distributed admit of this 

and U by con- „ -on, 

traposition, sort of conversion. Thus, 



A. " All men are rational/' may be converted into 

E. " Whatever is not rational is not a man." 

U. " All men are rational animals," may become 

E. " Whatever is not a rational animal is not a man." 

17. U may be converted simply. Thus, "All 

men are rational animals." Therefore, 
U converted 

simply and " All rational animals are men/' This is 

t ence in o . ^ an( j ^ su i :)a ite rna tion will give I also. 

Y may be converted into A, which by subalter- 

nation yields I. Thus, "Some men 

are poets" {i. e. all the poets), yields A, 

All poets are men. 

18. The several kinds of judgments therefore 
Summation may be converted as follows : 



Sec. IV.} IMMEDIATE INFERENCE. H7 

A may be converted into Y and thence I. 
E into E, and thence O. 
I into I. 

O into I indirectly by contraposition. 
U into U, and thence I. 
Y into A, and thence I. 

A and U may also be converted by contrapo- 
sition. 

Sect. IV. — Other Modes of Immediate Inference. 

19. Besides Opposition and Conversion, the 
standard modes of Immediate Infer- M m 

Other forms of 

ence formerly recognized by logicians, Immediate In- 
several other forms of it deserve men- 
tion. 

A. By Keciprocal Change of Positive and 
Privative Conceptions. 

20. If we take any pair of Positive and Priva- 
tive, or as they are styled by some, 
Infinitated Conceptions, as has before tive and Priva . 
been shown, they comprise, taken abso- tlve Concep- 

J L \ tions, 

lutely, all being, or the universe : and 
taken most narrowly, they include all the members 
of the genus which is the particular object of 
thought. Thus " virtuous" and "not virtuous/' 



118 LOGIC. [Chap. IV. 

taken absolutely, include the universe of actual and 
possible being. But practically, they are only used 
in reference to beings capable of virtue, i. e. moral 
beings, and, in ordinary cases, are applied to none 
but mankind. Supposing the latter to be spoken 
of, all are included in the virtuous and non-virtuous, 
and whatever men are not one are the other. 
To affirm the Therefore, to affirm a Positive Concep- 
Positive is to tion of any subject, is the same as to 
tive and vice deny its corresponding Privative, and 
versa, v ^ ce vers(lt It is often convenient in 

such cases, instead of an awkward and confusing use 
of the particle " not," in order to mark the Priva- 
tive contradictory, to use the particles in or un to 
form a single compound privative word — as incon- 
sistent for not consistent, imwise for not wise — or to 
use any word of corresponding privative import, 
without any explicit negative particle, as foolish for 
unwise, soft for not hard* 

Bales for snch ^1. This sort of immediate inference 
Conversion. j s governed by the two following rules. 
a. If the predicate be changed from Positive to 
Privative, or the reverse, change the quality of the 
judgment. Thus, "all men are rational," "no men 



Sec. IV.] IMMEDIATE INFERENCE 119 

are (not rational), i. e. irrational/' and by conver- 
sion, "no irrational beings are men/' 

6. To change the subject in like manner, first 
convert the proposition : thence change the subject 
(now become predicate), from positive to privative 
or the reverse, and change the quality of the judg- 
ment. Or, (what is the same), convert the judgment, 
and proceed as in rule first. Thus, 

" Some men are (all the) poets." By conversion, 

"Some (or all) poets are men." 

" Some (or all) poets are not beings who are not men." 

" No trees are stones." By conversion, 

" No stones are trees." 

" All stones are things not trees." 

These methods of immediate inference may be 
applied to all the varieties of propositions. 

B. Immediate Inference from*Disjuncttves 
or Partitives. 

22. In a Disjunctive or Partitive Judgment, it is 
immediately evident that whatever of 

From Disjuno* 

the objects included in it belongs to tives and Par- 
one of its members, is not included in 
any of the others, and whatever is not included in 
it, does belong to one of the others. Thus, u The 



120 LOGIC. [Chap. IV 

seasons are either Spring, Summer, Autumn, or 
Winter." "Spring is neither Summer, Autumn, 
nor Winter," and " whatever seasons are not Spring; 
are either Summer, Autumn, or Winter." 
C. From a Combination of Predicates. 

23. If it be known of man that he is rational, 

By uniting Pre- a ^ S0 *^at ^ e * s an l ma ^ a l so that he 

dicates. laughs, then these Predicates may be 

united in one judgment, which may be A or U, ac- 
cording to circumstances — in the present case U — 
Thus : " Man is a rational animal that laughs." 
Other Formulae furnish materials for immediate 
inference too numerous and obvious to 

Other Pormnlse. . . . n lt TT , 

require minute specification. " Howard 
was a philanthropist," therefore philanthropy has 
a real existence. " The President is the supreme 
executive," therefore to assail the President is to 
assail the supreme executive. 

24. Some have maintained that these processes of 

Immediate Inference are unimportant, 

The importance , . , , . . . , . 

of Immediate because the conclusion contains nothing 

Inference no £ previously contained in the premise, 

showni 

But if this objection be valid it lies 
against all reasoning. It is further objected that 
the conclusion is identical with the premise. This 



Sec. IV.] IMMEDIATE INFERENCE. 121 

is an error. It will hardly be claimed in regard to 
inference by opposition, especially con- 

J # J Conclusion not 

tradictory opposition. In conversion Identical with 
the subject or principal notion on the e reml e ' 
judgment is changed. Equivalent changes from 
the premise to the conclusion occur in other forms 
of immediate inference. Few persons who have not 
made Logic a study, can state with accuracy the 
exact illative converse of any, especially of all the 
fundamental logical judgments, as they understand, 
who have had experience in teaching Logic. Aji 
eminent logician says, u Could any person not accus- 
tomed to exercises of this kind, draw out fully all 
his own meaning, when he utters the simplest pro- 
position? The judgment 'all men Explication of 
are inortaP (a plainer cannot be found), " An men are 

. mortal," into 

tells us that man is one species in the other juag- 

class of mortal beings — that the mark ments> 

of mortality should always accompany our notion of 

man — that the word mortal is a name which may 

rightly be given to man — that, if all are mortal, 

any one man is — that any statement which affirms 

that no men are mortal, must be quite false — that 

even the statement that some men are not mortal is 

equally false — that since man is contained in the. 
n 



122 LOGIC. [Chap. IV, 

class of mortal beings, which is a wider class, it 
would be wrong to say all mortal things are men — 
that, however, the assertion " some mortals are men," 
would be true enough — even " some mortals are all 
men " — that no men can be immortal — that any im- 
mortal beings must be other than men — that mor- 
tality really exists, being found in man, whom we 
know to exist — that a man with immortal hopes is 
a mortal with immortal hopes — that (since heaven 
is immortality) a man expecting heaven is a mortal 
looking for immortality — that he who honors a 
man, honors a mortal. Thus from this simple 
judgment fourteen judgments have unfolded them- 
selves, or, as some would say, the judgment has been 
put in fifteen different ways, in the last three of 
which only is any new matter introduced. And 
yet any man of common sense would say that his 
proposition really implied them." — Thomson's Laws 
of Tkwgkt, pp. 191-2. 



CHAPTER V. 

REASONING MEDIATE INFERENCE. 

Section I. — Introductory Kemarks. 

Immemat^ Inference, as we have seen, is of 
one Judgment from another without the interven- 
tion of any third judgment or third term. 

1. Mediate Inference is from two judgments 
given as premises to a third founded Mediate Infer- 
upon them, in which the two terms of e T n ? is from tw ° 

*■ ' ■ Judgments giv- 

the conclusion are found to agree or en to a third. 
disagree with each other, through a third or middle 
term with which they have each been Through a Mid- 
compared in the premises. Thus, all ^ e Tem ' 
M is P, all S is M, .-. All S is P. Here all S is 
declared to be P, because it has previously been 
affirmed to be M, and all M to be P. Or if we 
take a negative conclusion, "No stones are trees, 
This oak is a tree, .*. It is not a stone." Here, 
oak, in the conclusion, is declared not to be a stone, 
because it is a tree, and no trees are stones. 

123 



124 LOGIC. [Chap. V 

2. It is obvious that the ultimate ground of 
Mediate Inference, as shown in the above examples 
(and the same may be shown of all others), is re- 
ducible to the principles of Identity and 

Founded on . . 

Identity and Contradiction or rather Non-contradio 
Contradiction, ,. -,- ,, n . -. -^ 

tion. J n the first case b and r agree — are 

one with each other, — because they each agree with, 

are the same as, M, Oak and stone do 

Ulnstration. . . ,, i ,i i ,i 

not agree with each other, because the 
one is, the other is not, a tree. To say that they 
are one, would therefore be a contradiction. 

3. This process of reasoning from two judgments 
given, to a third derived from them, through a 

middle term, is called an Argument, 

(from Argumentum, proof) and, when 

stated in regular logical form, so that the connection 

of the premises with the conclusion is immediately 

evident, it is called a Syllogism, ouXXo- 

ycfffio^y i. e. collecting the elements 

given in the premises into a conclusion. 

4. The subject of investigation now before us, 
therefore, is the doctrine of Syllogisms. 

A Syllogism, like all other reasonings, consists of 
Parts of the two P ar ts, that which is to be proved, 
Syllogism. an( j fa^ ty w hich it is to be proved 



Sec. I.] MEDIATE INFERENCE, 125 

Of these, in whatever order they may stand, the 
latter are called the Premises. These 
Premises are Major and Minor. 

The Major Premise is that in which the Major 
Term is compared with the Middle, 

, . i ii i -I • i Major Premises 

whatever may be the order in which 
they stand. 

The Minor Premise is that in which 
the Minor Term is compared with the 
Middle. 

The Premises, as the word implies, are put 
before the Conclusion, when the syllo- ^ a OT> . 

? J ^ Order of Premi- 

gism is arranged in regular logical ses and Oonclu- 
order. Thus : 

" All conquerors are tyrants. 
Buonaparte was a conqueror. 
He was a tyrant." 

In this case the Conclusion is connected with the 
Premises by some inferential particle, such as 
" therefore/' " hence," etc. 

But it is more common, and quite as natural, to 
ad )pt the reverse order in actual reasoning — to put 
the Conclusion first and the Premises afterward. 
Thus : " Buonaparte was a tyrant for he was a con- 
queror, and all conquerors are tyrants." And fre- 



126 LOGIC. [Chap. 7 

quently, in either case, not more than one premise ia 
expressed, the other being understood and obvious. 
Thus : " Many voters are tools of demagogues be- 
cause they are ignorant." " Free government will 
continue since the people are virtuous." This, re- 
gularly drawn out would be, 

" A virtuous people will preserve a free government. 

This people is virtuous. 
.'. It will preserve a free government." 

A Syllogism in which the premises are stated 
first is called Synthetic, because it puts 

Synthetic and 

Analytic Syllo- together the premises in order to form 
gisms. ^ e conclusion. 

When the conclusion is stated first, it is called 
Analytic, because this conclusion is analyzed into the 
proofs out of which it grows. 

The Major Term is the predicate of 

Major Term. ., ~ , . 

the Conclusion. 

The Minor Term is the subject of the 

Minor Term. ~ , 

Conclusion. 
Hence every Syllogism must have three, and but 
Hasthree Jndg- three > Judgments. The Major Premise, 
ments. the Minor Premise, and the Conclusion 

in which the major and minor terms are compared 
with each other. 



Sec. I.] MEDIATE INFERENCE. 127 

Every Syllogism must have three, and but three, 
Terms; the Major, Minor, and Middle. 

Th.r66 Tptttisi 

If there be four Terms, either in form 
or in fact (from the ambiguity of either of them), 
the two terms of the conclusion will not have been 
compared with one Middle Term, and no conclu- 
sion can follow. 

5. From the principles of Identity and Contradic- 
tion, the following Canons for testing Can(mg of the 
the validity of all Syllogisms result. Syllogism, 

a. If the Major and Minor Terms, each being 
compared with the same third or Mid- „ 

r Canon of Affir- 

dle term, both agree with it, they agree mative Conclu- 

with each other. This underlies all 

Affirmative Conclusions. 

b. If of the Major and Minor Terms, both being 
compared with the same third term, one of Negative 
agrees and the other disagrees with it, Conclusions, 
they disagree with each other. This is the founda- 
tion of Negative Conclusions. Therefore if one 
premise be negative, the conclusion must be negative, 

c. If they both disagree with the same third 
term, no conclusion follows as to whether >T 

' Negative rre- 

they agree or disagree with each other, mises ghe no 
This is the case of Negative Premises, 



128 LOGIC. [Chap. V. 

from which there can be no Conclusion. Thus, 
from "A bird is not a sheep," "a robin is not a 
sheep" — nothing can be inferred. 

d. The Middle Term must be distributed at least 

once in the premises, otherwise the 
must be Distri- Minor Term may be compared with one 

part and the Major with another part 
of it. From, 

"Some men are poets, 
Some men are Indians," 

Nothing follows. 

Plurative Judgments, however, give rise to a 
peculiar class of valid Syllogisms with an undis- 
tributed middle. Thus : 

* Most men have some kind of religion. 

Most men are uncivilized, 
.*. Some uncivilized persons have some kind of religion." 

The same is true of numerically definite Judg- 
ments. Thus : 

u 60 out of this 100 are unreflecting, 

60 out of this 100 are restless, 
.*. 20 restless persons are unreflecting." 

e. No term may be distributed in the conclusion 



Sec. I.] MEDIATE INFERENCE. 12<J 

which was not distributed in the premises. This, 
which is Illicit Process, is furtively jr moit Pr0 . 
speaking of more in the conclusion cesSi 
than was contained in the premises. Thus : 

"All beasts are animals, 
Birds are not beasts, 
They are not animals." 

/. From Particular Premises, of which Y is not 
one * nothing can be inferred. With 

Particular pre- 

none but the particular judgments I mises give us no 
and O of the old logicians in the pre- 
mises, no conclusion can follow, because, if both 
were I, no term would be distributed, whence would 
result an undistributed middle. From "some men 
are heroes," and "some men are poets/' nothing 
can be inferred. If both premises be O, they are 
both negative, and no conclusion can follow. If 
one be O and the other I, the middle term must be 
the predicate of O in order to be distributed, and in 
that case all the other terms will remain undistri- 

* The following is a valid conclusion from the particular judg 
nients Y and I. 

Y. Some trees are all the oaks. 
I. Some oaks are white oaks. 
•\ Some white oaks are trees. 
I 



130 LOGIC [Chap. V. 

buted. But, one premise being negative, the con- 
clusion must be so likewise. This would distribute 
the major term in the conclusion, which by suppo- 
sition was undistributed in the premises. Illicit pro- 
cess results. Thus: 

"Some men are not cultivated, 
Some poets are cultivated, 
Some poets are not men." 

g. If either Premise be particular, the Conclu- 
Conclusion par- s i° n must be Particular. In other 
ticular when wor( j s a universal conclusion requires 

either premise x 

is so. both premises to be universal. 

If the universal conclusion be A, then the sub- 
ject of it must be distributed in the premises, and 
must therefore be the subject of one of them, since 
being both affirmative, neither can distribute the 
predicate. For the same reason the middle term 
will be undistributed in that premise, being then 
the predicate of an affirmative. Therefore the 
middle term must be the subject of the other pre- 
mise, which must also be universal, in order that it 
may be distributed. Thus a universal affirmative 
conclusion requires both premises to be universal. 

If the universal conclusion be E, then both its 
terms must be distributed in addition to the middle 



Bee. I.] MEDIATE INFERENCE. 131 

term in the premises. This requires both premises to 
be universal and one of them negative, or both nega- 
tive and one universal. The latter is impossible as 
no conclusion can come from two negative premises. 
Therefore the premises must be both universal. 

The principle that one negative or one particular 
premise renders the conclusion respectively nega- 
tive or particular, logicians have expressed by 
saying that the conclusion follows the weaker part. 
The whole of these canons have been condensed 
into the following Latin lines : 

" Distribuas medium nee quartus terminus adsit, 
Utraque nee prsemissa negans, nee particularis : 
Sectetur partem conclusio deteriorem, 
Et non distribuat nisi cum praemissa, negetve." 

This reasoning, however, applies only to syllo- 
gisms in the old Logical Judgments, A E I and O. 
Syllogisms with U or Y in the premises, may have 
universal conclusions with one premise particular, 
Thus: 

U. " All men are rational animals, 
Y. Some men are all the poets, 

All the poets are rational animals," 

A. " All men are rational, 
Y. Some men are all the Polynesians, 
All the Polynesians are rational." 



132 LOGIC. [Chap. V. 

U. " Animals are all bodies having sensation, 
Y. Some animals are all oysters, 
•\ All oysters have sensation." 

Sect. II. — Moods. 
{ For Moods as affected by Substitutive Judgments, see Appendix B.) 

6. The Mood of a Syllogism is the relation of its 
several judgments to each other, with 

Mood Defined. ^ . . 

reference to their respective quantity 

and quality, these being designated by the symbolic 

letters A E I O. The Mood of a syllogism, whose 

premises and conclusions are universal affirmatives 

thus becomes AAA. If the major premise were 

universal affirmative, the minor universal negative, 

and the conclusion universal negative, it would be 

A E E, etc., etc. 

The possible combinations of these four kinds of 

Number of propositions are of course 4 X 4- X 4 =. 

Moods. g4 # g u £ m0S £ f these are invalid as 

involving violations of some of the preceding canons. 
Thus E E E, E O O, and others, are bad on account 
of negative premises. IOO and others, for parti- 
cular premises. I E O, for illicit process. Sifting 
Only eleven ou * a ^ mo °ds ^at are thus invalid, only 
?alid Moods, eleven valid ones remain. And of these 
only a part are valid in any one figure. 



Bee. III.1 MEDIATE INFERENCE. 133 

Sect. III. — Figure. 

7. The Figure of a Syllogism depends upon the 
situation of the Middle Term in the premises. 

The Figures as fixed by Aristotle were three. 
The first and normal figure is when the Figrnesof.Aris- 
middle term is the subject of the major totle ' 
and predicate of the minor. In the second, the 
middle term is the predicate of both, and in the third 
the subject of both. The fourth, which is reputed 
to have been introduced by Galen, and is largely 
dropped by logicians as an awkward and useless in- 
version of the first, occurs when the middle term is 
made the predicate of the major, and subject of the 
minor premise. Taking S, M, and P, respectively, 
for minor, middle, and major terms, the figures 
would be represented thus : 

1st Fig M P. 2d. P M. 3d. M P. 4th P M. 
S M. S M. MS. MS. 

S P. S P. S P. S P. 

Sub. Prae. ; Turn Prae. Prae. ; Turn Sub. Sub. ; Turn Pr«. Sub* 

8. Of the eleven valid Moods, some are Invalid 
in one figure which are valid in another, y^ aJld ^ 
Thus A E E would be valid in the valid Mooda - 
second figure, as, 

12 



134 LOGIC. [Chap V. 

" All men are mortal, 
No angels are mortal, 
V No angels are men." 

But in the first figure, it would involve illicit 

process of the major term. Thus : 

" All birds are animals, 

No reptiles are birds, 

•\ No reptiles are animals." 

The only valid moods in the first figure are A A 
A, E A E, A 1 1, E I O. As this is the figure into 
which the normal syllogism falls, logicians have 
usually unfolded the principles which govern the 
syllogism primarily with reference to that, and have 
devised ways of converting syllogisms in the other 
figures into it, and subjecting them to its tests. The 
canons which have been presented, however, apply 
immediately to the syllogisms in all the figures. 

9. As is their wont, logicians have wrought out 

mnemonic lines in Latin to designate the valid 

moods and syllogisms in the several figures, with 

the modes of reducing the subordinate figures to 

the first. 

w m rbArbArA, cElArEnt, dArll, fErlOqne prio- 

Figure l.« 

*• ris. 

tt rcEsArE, cAmEstrEs, fEstlnO, bArOkO (or 
Figure 2.< 

v fAkOrO), secundae. 



Bee. III.] MEDIATE INFERENCE. 135 

Figure 3. - 



"tertia, dArAptl, dlsAmls, dAtlsI, fElAptOn, 
bOkArdO (or, dOkAmO), f ErlsO, habet, quarta, 
insuper addit, 

fbrAmAntip, cAmEnEs, dlmAarls, fEsApo 



Figure 4. , 
* I frEsIsOn 



In the foregoing lines the vowels signify the 
moods of the syllogisms respectively al- 
lowablein each figure. The initial letters Mnemonic 
b, c, d, f, denote that the syllogisms 
having them in the lower figures are to be reduced 
to the corresponding ones in the first, m indicates that 
in doing this, the premises are to be transposed, s 
and p that the proposition denoted by the vowel 
immediately preceding, is to be converted, s, simply 
jp, per accidens, i. e. by limitation of quantity from 
universal to particular. 

10. A slight examination of the three first figures 
— and for practical purposes the fourth _. . . 

* ■"■ x Limitations 

may at present be passed by — will show npon the several 
that, in the First Figure, the minor pre- sures 
mise must be affirmative in order to Upon the 1st. 
escape illicit process of the major term 
or negative premises, and that consequently the 
major premise must be universal in order to distri- 
bute the middle term. The Second Upon the 2d. 



136 LOGIC. [Ohap. V 

Figure can prove only negatives, because the mid- 
dle term, being a predicate in both premises, re- 
quires at least one negative premise 

ponte ' to distribute it. The Third Figure 
yields only particulars, because the major and minor 
terms, being both predicates, can only be distributed 
by having their respective premises negative. But 
only one of these can be negative, and if either be so 
it must be the major, for if it be the minor, it will 
make the conclusion negative, and thus distribute 
the major term, which, in this case, would be un- 
distributed in the premises — thus bringing in illicit 
process of the major. 

11. It must, how 7 ever, be remarked, that these 
Exceptions to properties of the several figures will be 
t e oregomgin ~ rea £iy modified in the case of the judg- 

tne case of pre- ° J J ° 

mises U and T. ments in U and Y, which afford dis- 
tributed affirmative predicates, and therefore cure 
all faults of the syllogism arising from the non- 
distribution of affirmative predicates. Inasmuch 
as it does not appear from the mere form of ex- 
pression that any affirmatives distribute their 
predicates, it is alw r ays presumed that they do not, 
unless proved by other evidence. The analysis of 
the normal syllogism and its properties is therefore 



Bee. III.] MEDIATE INFERENCE. 137 

conducted on this presumption. But if the judg- 
ments usually classed as A and I, can in any case be 
shown to be U and Y in the syllogism, then neither 
of the foregoing limitations in respect to the several 
figures will hold. Thus, with these substitutive 
judgments, as premises, the first figure may have a 
negative minor without either illicit process or 
negative premises. Take the example, 

U. " All men are (all) rational animals, 
(Negative Minor.) E. No angels are men, 

No angels are rational animals.-* 
Again, 
(Particular Major.) "Some poets have genius, 

Y. Some men are (all the) poets, 
Some men have genius." 

Again in the second figure, 

U. " Eational animals are men, 
A. Poets are men, 
(Afiir. Conclusion.) ,\ Poets are rational animals." 

Also in the third figure, 

" All men are mortal, 
U. All men are (all) rational animals, 
(Universal Con.) A. ,\ All rational animals are mortal." 

This is the proper formula of the Inductive Syl- 
logism, which naturally falls into the Formula of la- 
third figure, and could not, aside from a gi sm , 
12* 



138 LOGIC. [Chap. V, 

substitutive judgment, yield a universal conclu- 
sion. Thus : 

"XYZ, are ruminant, 
XYZ, are (as good as) all horned animals, 
.*• All horned animals are ruminant." 



Sect. IV. — Maxims by which different logicians have 

APPLIED THE PRINCIPLES OF IDENTITY AND CONTRADIC- 
TION to the Syllogism. 

12. Most of these are founded on the prin- 
Genus Predica- ci P le that > in a normal judgment, the 
ted of Species, Genus is predicated of the Species, and 
therefore that the extension of the subject is included 
in that of the predicate. 

A. First among these maxims is the celebrated 
Aristotle's Die- Dw&wm* of Aristotle, that whatever can 
tum * be predicated affirmatively or negatively 

of any class or term distributed, can be predicated 
in like manner of all and singular the classes or in- 
dividuals contained under it. This is self-evident. 
Whatever can be affirmed or denied of all men, can 
be affirmed or denied of whatever is contained un- 
der the class man. This maxim is 

Directly appli- 
cable to First directly applicable to, and illustrated 

Figure ' by the First Figure. Thus : 



Sec IV.] MEDIA TE INFERENCE. 1 39 

" All men are mortal, 
Poets are men, 
.'. Poets are mortal." 

Here mortal, being affirmed of the genus man, is 

also affirmed of the species poets included under 

" Xo men are brutes, 
Poets are men, 
.'. They are not brutes." 

Here, what is denied of the higher class, is also 
denied of the lower class or species included in it. 

B. An equivalent maxim is that founded on the 
relation of Whole and Parts, that what mole and 
may be affirmed or denied of a whole PartSi 

(in extension), may be likewise of its parts, i. e. 
what is predicated of a genus may be predicated of 
the species and individuals, or the parts com- 
posing it. Pars partis est pars totius. 

C. To the same effect is the maxim contention 
contenti est contentum continentis. Men, the content 
of biped, is also the content of animal, which con- 
tains biped. 

D. Kant's formula is, nota notce est nota rei ipsius. 

This probably has reference to construing and testing 

Syllogisms according to the Intension of _ ± , ___ 
J ° to Intensive Syllo. 

the terms. To this some of the fore- gisms, 



1 40 LO GIC. [Chap. V. 

going maxims apply, but in a reverse order, since 
the whole of extension increases as the whole of in- 
tension decreases. Therefore, in the Intensive Syl- 
logism, the term of least extension, i. e. the minor, 
becomes the greater whole, and so in effect the major. 
Thus the Syllogism according to extension, 

" All conquerors are brave, 
Caesar was a conqueror, 
•\ He was brave," 

according to intension would be construed thus : 

* Caasar was a conqueror, i. e. had the mark or attribute of one, 
Conquerors are brave, i. e. have the mark of bravery, 
.He had the mark of bravery (was brave)." 

Construed either way, the connection of the same 
Conclusion the conclusion with the same premises, is 
b^ 6 Extension e( l ua Uy certain and necessary. Some- 
and Intension, times the Extension, sometimes the In- 
tension, is more prominent in the mind of the thinker. 

13. The relation of the several terms of the Syl- 

Ulnstration by l°gi sm to each other has often been ex- 
Diagrams, hibited to the eye by Circular Diagrams. 
Thus the Syllogisms of the several figures' may be 
exhibited. 



Sec. IV.l MEDIATE INFERENCE. \\\ 

Barbara. Celarent. 



1st Figure* 



1st Figniet 




Darii. 





Ferio. 




Cesare. 



Caraestres etc., etc. 



2d Figure, 





142 



8d Figure. 



LOGIC. [Chap. V. 

Darapti. Felapton, etc., etc 





For a fuller view of the different schemes of 
Syllogistic Notation, see Appendix B. 



Sect. V. — Unfiguked Syllogism. 
14. Before leaving this subject, it is proper 
£ow Figure dis- *° ca ^ attention briefly to a mode of 
appears. analyzing the Syllogism introduced by 

Hamilton, which dispenses with Figure altogether. 
After the explicit quantification of both terms of a 
judgment, the relation between them may be ex- 
pressed by the sign of equality, and either of them 
may become indifferently subject or predicate. In 
this way Figure disappears. If we say 

" Men are rational, 
Negroes are men, 
/. Negroes are rational." 



Sec VI.J MEDIATE INFERENCE. 143 

we may more explicitly, though awkwardly, state 
our meaning thus ; 

"All men are = some rational. 
All negroes are = some men. 
,\ All negroes = some rational." 

And it is obvious that the terms of either or all of 
these judgments may be transposed, without impair- 
ing the sense or reasoning. Thus : 

"Some rational = all men. 
Some men = all negroes. 
,\ Some rational = all negroes." 

All other figures may be similarly reduced. It 
is thus apparent that the Unfigured Syllogism ex- 
presses nakedly the essential principle which under- 
lies reasoning in all the Figures. 

►Sect. VI. — Hypothetical Syllogisms.* 
15. These are syllogisms in which the reasoning 

* The use of the terms "hypothetical" and " conditional/' as 
applied to judgments and syllogisms, varies with different logi- 
cians. Some use the word hypothetical to denote the genus, of 
which daey make conditional and disjunctive the species. 
Others make conditional the genus, which includes hypothetical 
and disjunctive as species. That is, different writers make the 
words hypothetical and conditional change places. 



144 LOGIC. [Chap. V. 

turns upon the Hypothesis in a hypothetical judg- 
K nin nient. A syllogism may contain hypo- 

Turns on the thetical judgments in which the rea- 
ypo esis. son i n g Joes no t ^ urn U p 0n the hypothe- 

Otherwise the . . . . 

Syllogism is S1S ; but simply retains it as one of the 

Categorical. termg of the conc l us i on . Thus : 

" Every man is either a hero or a coward, 
A. B. is a man, 
/. A. B. is either a hero or a coward." 

"The books of Scripture are entitled to reverence, if its authors 

are not impostors, 
The prophecies are books of Scripture, 
Therefore the prophecies are entitled to reverence, if their 

authors are not impostors." 

Such syllogisms are categorical. 

16. But when the Reasoning turns on the Hypo- 
thesis, the Syllogism is Hypothetical, and 
Syllogism De- becomes either Conditional, Disjunctive, 
or Dilemmatic, according as the Hypo- 
thetical Judgment on which it is founded, falls into 
one or the other of these classes. In these syllo- 
gisms the hypothetical judgment forms the major 
premise : one of its members affirmed or denied the 
minor — and the consequent affirmation or denial of 
some other member forms the conclusion. Thus : 



Bee. VIL] MEDIATE INFERENCE. 145 

"Major. If rains are plenty, the crops are plenty, 
Minor. The rains are plenty, 
The crops are plenty." 

Sect. VII.— Conditional Syllogisms. 
Conditional Judgments are founded on the prin- 
ciple of sufficient reason, otherwise „ 

x Grounded in 

called Reason and Consequent. Eeason and 

17. The nature of the Conditional onse ^ Tiei1 
Judgment thus being, that on the ground of Eea- 
son and Consequent, if the antecedent is true the 
consequent is true, it follows ; 

A. That, if the Antecedent be affirmed in the 

minor premise, the Consequent must be 

r ^ Laws of Condi- 

affirmed in the conclusion. tional Syllo- 

B. If the Consequent be denied, the glsm ' 
Antecedent must be denied, since, if the latter were 
true, the former would be so likewise. 

C. If the Antecedent be denied or the Consequent 
affirmed, no conclusion follows, for the latter may be 
true or the former false on other grounds. 

Of these the following are examples : 

A. IfAisBCisD, A is B, .'. C. is D. 

B. If A is B C is D, C is not D, .\ A is not B. 

c If A is B C is D, A is not B, .". no conclusion. 
'" I If A is B C is D, C is D, ,\ no conclusion. 
13 K 



146 LOGIC. [Chap.V. 

The fallacy of any inference in the cases under 
Fallacies ilhs- C > wil1 appear more plainly from con- 
trated, crete examples. Thus, if we deny the 

antecedent, the following example will show that 
nothing follows. 

"Jf James is a drunkard he is unfit for office, 
He is not a drunkard," 
.\ Nothing can be inferred. 

So likewise from affirming the consequent nothing 
follows. Thus : 

" If the people are virtuous they will establish schools, 

They will establish schools," 
.'. No inference is warranted. 

No fallacy is more common than that of drawing 
inferences in such cases. 

Sect. VIII. — Disjunctive Syllogisms. 
18. These are founded on the principle of Ex- 
ta eluded Middle. Of two Contradictories, 

Best on law of 

Excluded Mid- one must be true and the other false. 
There is no other alternative, no mid- 
dle ground. Genuine disjunctives are mutually 
exclusive. That is, each member excludes the 
others. Whichever is true, the others are false. If 
either be false, some one of the others is true. Thus, 
u it is either Spring, Summer, Autumn, or Winter/ 1 



Sec. VIII.] MEDIATE INFERENCE. 147 

Either of these excludes the others. Whichever is 

true, the others are false. Whichever is false, some 

one of the others is true. Hence with a disjunctive 

major ; 

First If either member of it be af- 

Laws of the Dis- 

firmed in the minor, the other mem- jnnctive Syl- 

bers are false. Thus : oglSII1, 

" Men are either angels, brutes, or rational animals, 

They are rational animals, 
/. They are neither angels nor brutes." 

This is what the logicians call modus ponendo 
tollens. 

Second. If, in the minor, either member of the 
major be denied, then some one of the other mem- 
bers is true. Thus, in the preceding example, if in 
the minor we say, " Men are not angels," it follows 
that they are either brutes or rational animals. 
This is modus tollendo ponens. 

19. It is proper to repeat that a Disjunctive 
may be turned into a Conditional by _, . 

* ' Disjunctives 

taking the contradictory of one of its turned into Con- 
members for the antecedent. "It is 
either Spring or Summer," is the same as " if it is 
not Spring it is Summer." Increasing the members 
thus: "It is either Spring, Summer, Autumn or 



148 LOGIC. [Chap. V. 

Winter" — we get by conversion, "if it is not Spring, 
it is either Summer, Autumn, or Winter." 

Sect. IX. — The Dilemma. 
20. The Dilemma is a syllogism having a Dilem- 
Dilemma De- ma ^ c Judgment for its Major Premise, 
fo^* with a Minor so affirming or denying 

some member or members of the major, as to lay the 
foundation for an inference. As this judgment is a 
combination of the conditional and disjunctive, so 
the Dilemma partakes of the characters of the con- 
ditional and disjunctive syllogism. The major pre- 
mise of the dilemma may be of various forms, each 
capable of different minor premises, and so furnishing 
a ground for different conclusions. 

A. The Major Premise may consist of one An- 
Different forms decedent with a Disjunctive Consequent. 
of the Dilemma, if A is B, either C is D or E is P. Affirm 

One Antecedent 

and a Disjunct- the Antecedent, A is B, and the Dis- 
ive Consent. j unctive Consequent, either C is D or E 

is F, follows. Deny the Consequent wholly, and the 
Antecedent must be denied. If neither C is D nor 
E is F, then A is not B. If, however, the Conse- 
quent be denied only disjunctively nothing can be 
inferred, for if either member of the Consequent be 



fiec. IX.] MEDIATE INFERENCE. I49 

true, the Antecedent may or may not be so. As id 
pure conditionals ; from the mere denial of the Ante- 
cedent or affirmation of the Consequent, nothing can 
be inferred. 

B. There may be a Plurality of Antecedents in 
the major, all having one Common Con- Plurality of An - 
sequent. If A is B, X is Y, and if C is ^ents "nd a 

x ' ' Common Conse- 

D, X is Y. quent, 

In this case, if the Antecedents be wholly or dis- 
junctively granted, the one Common Consequent 
must follow. For if either of the Antecedents be 
true, the Consequent is true. If the Consequent be 
denied, all the Antecedents must be denied. But 
from affirming the Consequent or denying either or 
all the Antecedents, nothing can be inferred. 

C. There may be a Plurality of Antecedents in 
the Major, each with its own Conse- plurality of An- 

quent. In this case, if the Antecedents te , ce 1 dents ' each 

* * with its own 

be affirmed wholly, the Consequents Consequent. 
may be affirmed wholly. If the Antecedents be 
affirmed disjunctively, the Consequents may be 
affirmed disjunctively. From the denial of Conse- 
quents wholly or disjunctively, the Antecedents 
may, in like manner, be denied wholly or disjunc- 
tively. But from any denial of the Antecedents or 

13* 



150 LOGIC. [Chap. V. 

affirmation of the Consequents, nothing can be in* 
ferred. 

" If men are virtuous they are wise, 
And if they are vicious they are unwise ; 
But they are either virtuous or vicious, 
.*. They are either wise or unwise." 

Or denying the Consequent disjunctively, 

" But either they are not wise or they are not unwise, 
.*. Either they are not virtuous or not vicious." 

That affirming the Antecedents or denying the 
Consequents wholly, would lead to a correspond- 
ing affirmation of Consequents or denial of Ante- 
cedents respectively, appears in the following ex- 
ample : 

" If A. B. is diligent he will prosper, 
And if C. D. is wise he will be diligent, 
But A. B. is diligent and C. D. is wise, 
.*. A. B. will prosper and C. D. will be diligent." 

In like manner the denial of both Consequents 
involves the denial of both Antecedents. 

Some Logicians, as Whateley, exhibit that alone 
as the only true Dilemma which has a 

Restriction of 

the Dilemma by plurality of Antecedents in the Major, 

some Logicians. -, -i* . ,. tv/t* 

& and a disjunctive Minor. 

21. The Dilemma has been named the Syllogis* 



Bee. IX., MEDIATE INFERENCE. 151 

mus Cornutus, or Horned Syllogism, because it con- 
fronts an adversary with two assump- Horng of ^ 
tions or arguments, on which it tosses Dilemma. 
him as on horns from one to the other, each being 
equally fatal to him. Hence the common phrase, 
" Take which horn of the Dilemma you will, it is 
equally fatal to you." Thus : 

" If things are what we can help, we ought not to fret about 
them, and if they are what we cannot help, we ought not to fret 
about them. But all things are either what we can or cannot 
help. .'. They are what we ought not to fret about." 

22. The names Trilemma, Tetralemma, Poly- 
lemma have been sometimes given to Trilemma Te- 
this sort of Syllogism according to the tralemma, etc. 
number of members or horns, if they exceed two. 
Thus: 

" If A is B, X is Y, and if C is D, X is Y, and if E is F, X 
is Y. But either A is B or C is D or E is F, .\ X is Y," is a 
Trilemma. 

23. The ultimate principles which determine 
the resolution of the Dilemma are those rjitimate prin- 
which determine the conditionals and ci P les - 
disjunctives out of which it is formed. 



152 LOGIC. [Chap. V 

Sect. X. — Incomplete Syllogisms. 

24. In ordinary reasoning, it is seldom that the 
process is fully expressed in a completed Syllogism. 
One of the premises is often wholly, and the other 

partially unexpressed. A syllogism 

Enthymeme. .,-, . , . 

with one premise unexpressed is an 

Enthymeme. Thus : 

" The Americans are a free people, 
.*. They are happy ." 

Here the unexpressed Major premise, 

" All free peoples are happy," 

is obvious. In this : 

"Bankers are wealthy, 
.*. A. B. is wealthy," 

r 

The Minor premise, 

" A. B. is a banker," 
is unexpressed. 

25. Enthymemes, like Complete Syllogisms, often 

express the conclusion with " because," 

lx\ VfliTlfiQ. iOTIUS 

or other equivalent particles, between 
it and the premise. Thus : 

" A. B. and C. are unfit to vote because they cannot read." 
The learner will readily complete such a Syllo- 
gism in regular form. Indeed the forms of En- 



S«c. XL] MEDIATE INFERENCE. \& c 

thymemes, occurring in ordinary speech, are in- 
numerable. Thus : 

" These men are good and therefore brave," etc., etc 

Sect. XI. — Complex Syllogisms. 
26. Several Syllogisms may be combined and 
abridged, so that the conclusiveness of the reasoning 
shall be just as evident as if they were all fully ex- 
pressed- Chief of this kiud is the 

SORITES, 

Or chain-syllogism, in which a number of syllo- 
gisms in the First Figure are so com- 
bined, that the predicate of the first pre- 
mise becomes the subject of the next, and so on, 
until, in the conclusion, the predicate of the last 
premise is predicated of the subject of the first. 
Thus: 

" The Hindoos are Asiatics, 
The Asiatics are men, 
Men are rational animals, 
Rational animals have body and spirit, 
. . The Hindoos have body and spirit." 

The conclusiveness of this may be represented 
thus: 



154 



LOGIC. 



[Chap. V 




27. The following principles control the Sorites. 
Principles and A. The several unexpressed proposi- 
laws of Sorites, tions are respectively conclusions of 
each next preceding syllogism. Each of them be- 
comes in turn the minor premise of the next follow- 
ing, as will easily appear by completing the several 
syllogisms. r 

B. All the intermediate expressed premises, 
therefore, between the first and the conclusion, are 
major. The first alone is minor. 

C Hence no premise except the first can be par- 
ticular, for the first figure must always have a uni- 
versal major in order to distribute the middle term. 

D. Hence, again, no premise can be negative ex- 
cept the last ; for a negative premise would make the 
conclusion negative, which in turn would become the 
uegai ive minor premise of the next svllogism. This 



Sec. XI.] MEDIATE INFERENCE. J 55 

has been shown, in the first figure, to beget illicit 
process of the major, and is not allowable.* 

GOCLENIAN SORITES. 

28. This is a form of the Sorites, so named be- 
cause it was first invented or brought 

, ^ , . Ti • i • Inverted Sorites. 

to view by Goclenius. It simply in- 
verts the order of the premises as found in the com- 
mon Sorites. Thus, if we take the example before 
given, it can be stated as follows : 

"Rational animals are composed of body and spirit, 
Men are rational animals, 
Asiatics are men, 
The Hindoos are Asiatics, 
,\ The Hindoos are composed of body and spirit." 

In this form of Sorites, each preceding subject 
becomes the predicate of the next, until, in the con- 
clusion, the predicate of the first premise is predi- 
cated of the subject of the last. The last premise 
alone may be particular, and none but the first can 
be negative. 

* These conditions, however, are subject to any exceptions 
which might arise from substitutive judgments in any of the 
premises. So also of the Sorites in every form. 



156 LOGIC. [Chap. V 

HYPOTHETICAL SORITES. 

Hypothetical 29 - Xt is P lain tliat a Sorites may be 

Sorites. conditional as well as categorical. Thus • 

If A is B, C is D, 

If C is D, E is F, 

If E is F, X is Y, but A is B, 
•\ X is Y. (Modus ponens), or X is not Y. 
•\ A is not B. (Modus tollens). 

In regressive form thus: 

If E is F, X is Y, 
If C is D, E is F, 

If A is B, C is D. But A is B, .\ X is Y. 
Or X is not Y. .\ A is not B. 
terect Form. If A B is virtuous, he is brave, 
, If brave, he is magnanimous, 
If magnanimous, he will do noble deeds, 
But he is virtuous, ,\ he will do noble deeds. 

PROSYLLOGISM, EPISYLLOGISM AND EPICHEIREMA. 

30. The different forms of complex Syllogisms 
comprise the modes in which separate syllogisms 
are combined into wholes of connected reasoning. 
In these the Sorites is rare. The Prosyllogism and 
Episyllogism are of constant occurrence. 

The Prosyllogism is one whose conclusion fur- 
Prosyllogism, nishes a premise for the principal argu- 
Episyllogism. ment. The Episyllogism makes the 



Bee. XL] MEDIATE INFERENCE. J57 

conclusion of the main argument one of its pre- 
mises. 

"Useful studies ought to be pursued: 

Prosyllogism. 
Logic is a useful study (since it helps to think well), 

Episyllogism. 

,\ It ought to be studied, and (hence an educational course 
which omits Logic is deficient)." 

31. Epicheirema denotes a Syllogism which has 

a Prosyllogism to establish each of its 

nr, Epicheirema. 

premises, lhus: 

"Man has a spirit, for he is rational, 
And he has a body, for he fills space, 
,\ Some thing that has a spirit has body." 

This name is also applied sometimes in cases 
where there is a single Prosyllogism. 

Polysyllogism is a combination of several syllo- 
gisms in one argument. The Sorites is 

/» . . Polysyllogism. 

one species of it. 

14 



CHAPTER VI. 

APPLIED LOGIC — FALLACIES. 

1. Having brought to view the fundamental 
Transition to laws of P ure thinking, or principles of 
Applied Logic. Formal Logic, as related to Concep- 
tions, Judgments, and Reasonings, it remains that 
we now treat, as briefly as possible, of the applica- 
tion of these principles, first to the 

Fallacies 

detection and avoidance of errors in 

thinking; and next, to the right conduct of the 

thinking process, when employed in the 
Methodi ,. n . . 

discovery of truth as pertaining to 

actual being. The former brings us to the doctrine 

of Fallacies, the latter of Method.* And first, 

Section I. — Fallacies. 

2. A Fallacy is any unsound or delusive mode 
Fallacies de- of reasoning, which wears a specious 
fined. appearance of being genuine, and thus 

often has power to impose upon men. 

* For a fuller exhibition of the difference between Formal ani 

Applied Logic, the student is referred to the observations on thii 

Bubject in Chap. I., Sect. IV. 
158 



Sec. I.] FALLACIES 159 

3. Fallacies are divisible into Paralogisms and 
Sophisms. A Paralogism is a fault in Divided into Pa- 
reasoning: unknown to him who em- * ao £ lsms ?f 

° Sophisms. De- 

ploys it. A Sophism, or sophistical nnitionofeach. 

reasoning, is a faulty argument understood by him 

who employs it, and used for the very purpose of 

deceiving. It is proper to add. how- „ , f 

& ... Botn have tne 

ever, that these distinctions have no same Logical 

logical, whatever may be their moral 
significance, and that they are often overlooked by 
good writers who use the terms Fallacy, Paralo- 
gism, and Sophism interchangeably and indiscrimi- 
nately. x 

4. Fallacies are further divisible into Formal 
and Material. The former are those 

Formal and Ma- 
in which no conclusion follows from the terial Fallacies 
i .-, t distinguished, 

premises, however there may be an ap- 
pearance of it. These are all cases of more than 
three terms, Undistributed Middle, II- Instances of 

Formal Falla- 

licit Process, Negative Premises, affirma- c i es , 

tive conclusion with either premise negative,* 

* It is important, however, to remember that many proposi- 
tions, in form negative, are not so in the fact, because the force 
of the negative particle falls on the subject or predicate instead 
of the copula. Propositions are in reality negative only when 



160 LOGIC. [Chap. VL 

making any conclusion from particular premises, 01 
a universal conclusion when either premise is par- 
ticular, except when Substitutive Judgments furnish 
the necessary distribution of terms,* from denying 

the real import of the copula is negative, so dividing the two 
terras from each other. Thus : 

" He who has not enough is not really rich, 
No miser has enough, 
.*. No miser is really rich." 

The minor premise is really equivalent to 

" All misers are persons who have not enough, 
,\ All misers are persons not really rich." 

" No person who is not secure is happy, 
No tyrant is secure = All tyrants are persons not secure, 
.*. No tyrant is happy." 

Where both premises are really negative such an experiment will 
not succeed, 

" Vicious persons are not happy, 
A and B are not vicious, 
•\ No conclusion." 

All attempts to transfer the negative particle to one of the terms 
here, will result in Four Terms, or Undistributed Middle, or in 
altering the meaning of one premise. 
* Such an exception is the following: 

" Some mortals are (all) men, 
Some men are (all the) poets, 
.\ All the poets are mortal." 



Sec. L] FALLACIES. 161 

the Antecedent or affirming the Consequent of a con- 
ditional ; and from violating any of the canons of in- 
ference in Disjunctives and Dilemmas : inferring A 
from A, or O from O, by conversion, etc. ; etc. These 
have been developed already under Formal Logic, 
and belong properly to it. They are vices in the 
very form of thinking, whatever be the premises or 
conclusion. They do not, indeed, belong to real 
thought, but only to the counterfeits 

Why introduced 

which simulate it. They enter into in Applied 
Applied Logic only as principles of oglc> 
Formal Logic which are applied to detect vices in 
reasoning about matters of actual being. Indeed, 
they would hardly need to be introduced here at all, 
were they always put in such phrase as to be palpa- 
ble. If apparent, the invalidity of the argument in 
which they occur is self-evident. They are, how- 
ever, very apt to be disguised under 

-, . n Often disguised, 

equivocal or vague expressions ; or, for 

other reasons, to elude the notice of those con- 
cerned. On this account they require to be noticed 
in Applied as well as in Formal Logic. 

5. Material Fallacies are such as occur when there 
is no fault in the reasoning process, and Material Fa iia. 
the conclusion does follow from the pre- cies Defin ed. 
u* L 



162 LOGIC. [Chap. VL 

mises. Hence called Material, because they lie not 
in the form, but the matter of the Syllogism. la 
n „ it asked, how is a fallacy possible 

Groundless pre- ? J r 

mise or irrele- here? The answer is, 1st, that a pre- 

vant conclusion. . , . . -, , n 

mise may be unwarrantably assumed, or 
2d, the conclusion may be irrelevant. It may fall 
short of what the reason er intends or professes to 
Ignoratio prove. The technical name of this lat- 
Elenchi. ^ er j s Jgnoratio Elenchi — ignorance of 
the proof of the real issue, the contradictory of 
your adversary's proposition which you undertake 
or assume to demolish. This is a fallacy of very 
frequent occurrence. It is a common defense of 
criminals to allege that they were insane ; and to 
attempt to prove this by showing that 
they acted very unreasonably ! But 
this is not to the purpose, for if it were, all crimi- 
nals would be maniacs, and guilt would be impos- 
sible. So it is a frequent and wicked practice of 
this fallacy or sophism, to arouse the passions of the 
tribunal appealed to in regard to the atrocity of an 
imputed offense, instead of proving it to have teen 
committed by the accused. 

6. To this head may be referred various argu- 
ments which logicians have been accustomed to con- 



Sec. I .] FALL A CIES. 163 

trast with argumentum ad rem, L e. to the point. 

Such is argumentum ad verecundiam, or Argument™ ad 

appealing; to the feelings of reverence r A e f* 
rr ° & Ad verecundi- 

for certain persons or objects, instead of am, 

proving the point in hand : argumentum 

7 . ,. • ,i , • Adignorantiam 

ad ignorantiam, assuming that your posi- 
tion is correct unless your adversary can evince the 
contrary : or it is sometimes used to denote any sort 

of sophism which imposes on men's 

, 7 Ad populum. 

ignorance : argumentum ad populum, 

which is very much akin, being addressed to the 

passions and prejudices rather than the intelligence 

of the people ; and finally argumentum 

, , . , . J , , . Ad hominem. 

ad hominem, an appeal to the practice, 
principles, or professions of an adversary, as con- 
firmatory of our own position or fatal to his. 

This argument is legitimate so far as concerns 
an adversary, and for the purpose of 

., . , . Tjy , , , How far valid. 

silencing him. It understood to be 
limited to this, it is not objectionable. So our 
Saviour often employed it to silence the cavils of 
the Pharisees and other adversaries. It is illegiti- 
mate when employed as if it established any propo- 
sition absolutely, or were binding upon any besides 
those whose personal opinions and conduct thus 



164 LOGIC. [Chap. VL 

make against their positions ; or even upon them, 
after they renounce such opinions and conduct. 

7. The other sort of material fallacy by the un- 
warrantable assumption of a premise, has some 
forms that have been signalized by corresponding 
names. Chief among these is, 

Petitio Principii or begging the question, which 
Petitio Princi- * s ^he unwarrantable virtual assumption 
pu \ of the thing to be proved, or of that by 

which it is to be proved, without proving it, in the 
coarse of the argument. Thus, if one undertake to 
show that a given tariff will be beneficial because it 
will promote the public wealth, without proving 
this latter, he perpetrates a petitio principii. The 
most deceptive form of this fallacy is, 

Arguing in a circle — argumentum in circulo — in 
Arguing in a which the conclusion is virtually used 
Circle. ^o p r0 ve the premise, thus going in a 

circle which returns upon itself, from premise to 
conclusion and from conclusion to premise. To 
argue that certain men are good because they be- 
long to an excellent party, and that this party 
is excellent because it includes such worthy mem- 
bers, is to argue in a circle. Some demonstrate 



Sec. L] FALLACIES. 165 

the immortality of the soul from its simplicity, 
and then its simplicity from its immortality. 

8. Non causa pro causa assumes that to be 9 
cause which is not a cause. Foremost No n causa pr< 
among these is the fallacy of post hoc caTLSa " 
ergo propter hoc, taking a mere antecedent of an 
event to be, as a matter of course, its cause. As if, 
because night precedes day, it were therefore the 
cause of day, or because civil war in the United 
States preceded the continental war between Aus- 
tria, Prussia, and Italy, it were therefore the cause 
ox that war.* 

9. An assumption analogous to this is the taking 
of non tale pro tali, assuming a resem- Non tale 
blance without proving it. Thus, "the tali ' 
season is favorable to apples because peaches are 
abundant," implying such a resemblance between 
these two kinds of fruit, and the requisites to their 
growth, as warrants such an inference. "All other 

* Notwithstanding the elaborate efforts of Mill, Brown, and 
ethers to prove that cause is only antecedent or invariable ante- 
cedent, the intuitive judgment of the human race is well voiced 
in the following words of Cicero. 

u Causa est ea quid efficit id cujus est causa. Non sic causa 
inteUigi debet, ut, quod cuique antecedat, id ei causa sit, sed quod 
cuique efficienter antecedat."— Quoted in Bowen's Logic, p. 306. 



166 LOGIC. [Chap. VL 

religions are delusions. Therefore Christianity is a 
delusion." 

Sect. II. — Fallacies partly formal and partly 

MATERIAL. 

10. By far the most numerous and misleading 
Semi- Logical class of Fallacies, are those styled by 
Fallacies. Whateley " semi-logical." This term 
has been criticized as absurd, as if there were no 
conceivable medium between a Fallacy purely 
The term Ex- logical* or non-logical. But whatever 
plained. ma y fa sa [^ f ^ e term, he employs it 

to denote a reality which no other term adequately 
denotes. It denotes the class of Fallacies arising 
from the ambiguous use of terms in reasoning, or in 
the syllogism. 

11. An Ambiguous Term is equivalent to Two 
. . .. Terms; consequently, if either of the 

An Ambignons L J 7 

Term=Two three terms of a syllogism be ambigu- 
ous, it amounts to bringing a fourth 
term into it. But when there are four terms there 
can be no conclusion. We see then how this Fal- 
Hcw Semi-Log- lac 7 of Ambiguous Terms is partly 
te&* material and partly formal. In order 

to detect the ambiguity, we have to look at the 



tfec II.] FALLACIES. 167 

matter of the syllogism as contained in the meaning 
of its terms. So far it is material. When the am- 
biguity is detected, the fault which gives rise to the 
fallacy, is shown at once to be formal, because the 
syllogism is loaded with four terms which are in- 
compatible with any conclusion. It is true that, at 
bottom and in essence, this fallacy is formal. But 
the discovery of it requires examination of the mat- 
ter embraced in the syllogism. Thus : 

" Feathers are light, 
Light is contrary to darkness, 
."• Feathers are contrary to darkness," 

is a syllogism in reality with four terms, two of 
which are words spelt with the same letters, but of 
different meanings. This difference of meaning 
must be ascertained in order to expose the fal- 
lacy. 

12. Fallacies of this description are far the most 
specious and numerous of all, and are g^ Fallacies 
as various as the various causes or kinds s P eci(ms ' 
of ambiguity in language. We will call attention 
to a few of the more prominent that logicians have 
been accustomed specially to designate. 



168 LOGIC. [Chap. VL 

13. The fallacy of Division and Composition. 
Division and I* 1 this the middle term is taken divi- 
Oomposition. dedly or distributively in one premise, 
and collectively in the other. Thus : 

"All these persons are a crowd, 
A, and B. are some of these persons, 
.*. They are a crowd." 

Here these persons are taken collectively in the 
major, and otherwise in the minor. 

" Five is one number, 
Three and two are five. 
.*, They are one number." 

This is composition in the major and division m 
the minor. 

14. This fallacy is of constant occurrence in con- 
Pallacy of the action with the word " all," which, in 
word 'all." ^he peculiar idiom of our language, 
affords great facilities for it. First, as in the ex- 
amples given above; 

" All these soldiers are an army, 
All these soldiers are individual persons, 
.*, Individual persons are an army." 

Here in the major "all" is taken collectively, in 
the minor distributively. 



Sec. IL] FALLACIES. 169 

But the greatest liability to an ambiguous or 
non-natural sense of the word " all," is 
where it is the subject of a negative 
judgment, in which case it is nevertheless impossi- 
ble to deny the predicate of "all" the subject. 

Thus: 

" Not all men are poets, or 

All men are not poets," 

is equivalent to 

"Not every man is a poet, or 
Some men are not poets." 

Sometimes there is danger of construing " not all" as 
equivalent to none, whereas it only amounts to 
" not some." This is well illustrated by Whateley 
in the following example : 

" If all testimony to miracles is to be admitted, the Popish 
legends are to be believed ; but the Popish legends are not to 
be believed ; therefore no (for " not all") testimony to miracles 
is to be admitted." 

It is important to be on our guard against fallacies 
arising from ambiguities in this pregnant mono- 
syllable. 

15. A very ensnaring form of ambiguous middle 

is known as Fallacia Accidentis, or „ „ , 

Fallacia Acci- 

a dicto secundum quid ad dictum sim- dentis. 

15 



170 LOGIC. [Chap. Vi 

plieiter, and vice versa, i. e. of using the middle 
term considered with reference to some of its acci- 
dents in one premise, and with reference to its mere 
essence in the other. 

" The covering of sheep is what we wear, 
Undressed wool is the covering of sheep, 
Undressed wool is what we wear." 

Again : 

" Government is a blessing, 

The most cruel despotism is a government, 
.\ Therefore it is a blessing." 

16. A very common form of ambiguous mid- 
Fallacy of Ety- dle is that founded on Etymology, or 
mology. ^ e assumption that derivative, paro- 

nymous, or conjugate words have the signification 
of their roots, and compounds of their originals. It 
is true indeed, that the meaning of words sometimes 
remains unchanged through all these variations. 
Sometimes the changes of meaning are slight, but, 
for that very reason, all the more liable to be over- 
looked and to gender fallacies. Thus : 

"Projectors ought not to be trusted, 
This man has formed a project, 
•\ He ought not to be trusted ' 



8ec. II.] FALLACIES. 171 

li Artful persons should be shunned, 
A. B. is a great artist, 
.• He ought to be shunned." 

" Truth is derived from to trow, i. e. believe, 

But belief is variable, 
\ Truth is variable, i. e. not immutable." 

17. Analogous to this is the Fallacy of Interro- 
gations, sometimes called Fallacia Plu- p a u aC y of In- 
rium Interrogationum. This is prac- terrogations, 
ticed when, under one question in form, by ambi- 
guity of meaning, more than one question in reality 
is put, so that the person questioned is entrapped, 
whatever answer he may give. This is a trick fre- 
quently practiced by examiners of witnesses. Law- 
yers are peculiarly prone to it. They put ambigu- 
ous and embarrassing questions, and then with 
great show of sincerity and fairness, insist on a 
categorical yes or no for answer, as if to refuse such 
an answer would imply a lack of truthfulness, when 
in fact, such a categorical answer must be false or 
inadequate, owing to the ambiguous implications of 
the interrogation. 

So the attempt is often made to ensnare or deceive, 
by a false assertion or implication, in a p^ impi^ 
question so put as to imply that it is tioils ' 



172 LOGIC. [Chap. VI 

beyond dispute. No better instance of this can be 
found than the celebrated question of Charles II. to 
the Koyal Society, "Why a dead fish 
does not, though a live fish does, add to 
the weight of a vessel of water in which it is placed ?" 
This was put with such apparent assurance that 
some of the philosophers w 7 ere, for the time, de- 
ceived, and busied themselves in seeking an expla- 
nation of the fact, while they omitted to inquire if 
it was a fact. So, many an innocent person has been 
entangled and led to criminate himself, being for the 
moment unmanned and thrown off his guard, by the 
very audacity with which such questions were put to 
him as these : " How long since you left off drinking, 
swearing, back-biting," etc. ? No duty is more in- 
cumbent on courts than that of protecting witnesses 
and parties against such injustice. 

18. Quite similar to this is the demand often 
a „ w made upon witnesses by examiners, not 

Demand for Dis- L ' 7 

tinct and Ade- only for a Clear, but for a Distinct and 

even Adequate Cognition (see chap. II., 

Sects. 9, 30) implying that their testimony is to be 

suspected, unless, besides certainty as to the object 

testified about, they can also give its 
Example. 

marks. Thus, if a witness testifies that 



Bee. II.] FALLACIES. 173 

a certain signature or manuscript is in a given man's 
hand-writing, it is quite common to insist that he 
6hould give some of the marks or distinctive pecu- 
liarities by which he distinguishes the chirography 
in question. The same thing is often done in ex- 
aminations for the purpose of identifying persons, 
places, and other objects. The fallacy of all this, 
so far as it implies distrust of the testimony of those 
who are unable to give the marks, is palpable. In 
general it is only the few experts, in each ybMblcj Ez- 
department, who, besides knowing ob- P osedi 
jects with certainty, can give the distinguishing 
marks or definitions of them. There are few things 
that we know with more certainty than the different 
hand-writings with which we have been familiar. 
There are few matters in respect to which those who 
have not made it a subject of special study, will 
more certainly and egregiously blunder, than in at- 
tempting to give the marks which distinguish the 
chirography of different persons. So with other 
things. Nothing would sooner nonplus such ques- 
tioners themselves than to exact of them a logical 
definition of words, or the marks of conceptions, with 
which they are perfectly familiar, and which they 
constantly use with substantial accuracy. 

15* 



174 LOGIC. [Chap. VJL 

19. Another fallacy is the Over-estimation of 
Probabilities, i. e. of the degree of belief which 

Over-estimation ou g ht to be produced by evidence less 
of Probabilities, ^} ian cer tuin — especially of supposing 
that a plurality of probabilities necessarily strengthen 
each other. A single probability of any uncertain 
event is ascertained by dividing the number of chances 
favorable to the event by the total number of chances. 
Thus the probability that a person blindfolded will 
take a black ball out of an urn containing 10 white 
and 2 black balls is -^ or |. 

20. " To find the chance of the recurrence of an 
event already observed, divide the number of times 
the event has been observed, increased by one, by the 
same number increased by two. If an inlander coming 
to the sea, observed the phenomenon of the tide 
ten times in succession, the chance to him that at 
the next period the tide would again rise would be 
Tir+i = TT; or 11 to 1. Every certainty is repre- 
sented by a unit, as has been shown ; and so many 
units are added to the possible cases (denominator 
of the fraction) as there have been events, and so 
many to the favorable cases (numerator) as there 
have been favorable events. i Or, if we represent/ 
says M. Quetelet, 'the number of times that IVj 



Sec. II.] FALLACIES. 175 

event lias occurred by a similar number of white 
balls that we throw into an urn, adding also one 
other white ball and one black ball, the probability 
of the reproduction will be equal to that of drawing 
a white ball/ 

"In order to calculate the probability that an 
event already observed will be repeated any given 
number of times, the rule is, to divide the number of 
times the event has been observed, increased by one, 
by the same number increased by one and the number 
of times the event is to recur. Thus, if the tide had 
been observed 9 times, the chance that it would re- 
cur ten times more would bef- +1 o+T = (to") = h 
1 This is the same thing as if each reproduction of 
the observed event corresponded to putting a white 
ball in an urn where there were already, before 
commencing the trials, a white ball and as many 
black balls as it is supposed that the event observed 
should re-occur times/ " — Thomson' sLaws of Thought. 

21. If two or more probabilities are independent 
of each other, they do afford mutual fcth 
support. But if otherwise, if they are strengthen and 

when they 

probabilities of probabilities, they weak- weaken each 
en each other. If the credibility of a ot]iQXt 
witness be f so far as his ability to observe aright 



176 LOGIC. [Chap. VI. 

and know the facts is concerned, f so far as his 
veracity is concerned, then the total probability of 
his telling the truth is f X f = tq, unity being the 
representative of certainty. 

22. If, however, the probabilities are mutually 
independent, they strengthen each other, and as 
they increase in number and force, they may come 
short of certainty by only an infinitesimal distance. 
Thus, if the probability that A. B. committed a 
given murder be strong, 1, from certain money be- 
longing to the victim being found in his possession ; 
2, from his boots fitting tracks found near the 
place of murder; 3, from blood on his clothes; 
4, from a piece of knife-blade found in the head of 
the murdered body fitting precisely the broken 
blade of a bloody knife found in the pocket of the 
suspected person ; it is clear that all these separate 
probabilities confirm each other, and together fall 
only short of apodictic proof. In this case, the mode 
of computing the absolute probability, is to sub- 
tract each separate probability from unity, which 
gives the probability of the opposite event, or of 
failure arising from each several cause. But as these 
several probabilities of the opposite event weaken 
each other, or are probabilities of probabilities, the 



Sec. II.] FALLACIES. 177 

entire probability of it is ascertained by multiply- 
ing the separate ones together. This product sub- 
tracted from unity will give the probability of the 
original event in question, of which this is the oppo- 
site.* Thus in the example just given ; let the 
first probability be ^, the second -^, the third. J, the 
fourth §. Subtracting each of these from unity, 
and multiplying them together, we have |-Xf Xf X 
J = -^- = -i-, which, subtracted from 1, gives yf , as 
the probability that the suspected person was the 
real murderer — a probability sufficient to neutralize 
all reasonable and practical doubt. 

23. Strictly, however, this and all positive direc- 
tions touching the calculation of proba- „ , , , , 

° x Strictly belongs 

bilities, belong to the doctrine of Me- to Logical Me- 
thod. It comes in here very naturally, 
however, in connection with the correlate fallacy. 

* "As, in the case of two probable premises, the conclusion is 
not established except on the supposition of their both being true, 
bo in the case of two (and the like holds good with any number) 
distinct and independent indications of the truth of some propo- 
sition, unless both of them fail, the proposition must be true , we 
therefore multiply together the fractions indicating the proba- 
bility of 'failure of each, — the chances against it; and the result 
being the total chances against the establishment of the conclu- 
Bion by these arguments, this fraction being deducted from unity, 
the remainder gives the probability for it." — Whateley's Logic, 

Book III., 15. 

M 



178 LOGIC. [Chap. VL 

24. A source of ambiguity, not only in the 
. _. . „ middle, but other terms, which ought 

Ambiguity Fie- 7 7 ° 

t» Universali- not to be overlooked, although the 
means of guarding against it, will more 
fully appear under the head of Induction, has re- 
ceived the name fictce universalitatis .'. i. e. of a 
groundless inference from a few cases to all cases. 
This is among the most common forms of delusive 
and fallacious reasoning. Common Ex- 
amples of this are, that Friday is an 
unlucky day, because some enterprises begun on that 
day have suffered disaster: that an epidemic is 
raging, when only the fewest cases of disease have 
appeared : that hemorrhage of the lungs is always 
fatal, because it is often so : that all men are knaves 
because so many are : that the whole community are 
of a given opinion, because A. B. and C. have ex- 
pressed it. Out of such fictitious universals arise 
Syllogisms like the following : 

" Men love to be humbugged; 
The President of the Bible Society is a man, 
.*. He loves to be humbugged." 

25. The sources of ambiguous middle are as 
m . . numerous and varied as the sources of 

Sources of Am- 

>»jgnoas Middle, ambiguity in language itself. Their de- 



Seu III.J FALLACIES. 179 

tection and correction belongs rather to rhetoric, 
grammar, or philology, than to logic. We have no 
room to pursue it further here. Those who desire 
to see it unfolded at greater length, may consult the 
chapter on Fallacies in Whateleifs Logic with in- 
terest and profit. 

26. It only remains that in concluding the sub- 
ject of Fallacies we present some specimens of 

Sect. III. — Logical Puzzles. 
In inventing which the intellectual activity of 
past times exerted itself, for lack of . , „ , 

J Logical Puzzles 

worthier objects. These have been be- more ingenious 

., t . -,. A . . than useful, 

queatned to succeeding generations to 
task their subtlety, and at once amuse and perplex 
students in their leisure hours. This however has 
not been the worst of it. They have gone far to 
countenance the impression that Logic, instead of 
being a genuine or useful science, is little better 
than a kind of jugglery and legerdemain, for work- 
ing up seeming demonstrations of manifest absurdity 
and falsehood. 

27. The Dilemma is a favorite instru- „ r , „ 

use of the Di- 

ment for this sort of logical sleight of lemma for tbj 
hand, A sly fault in some member of purpase ' 



180 LOGIC. [Chap. VL 

its complex parts affords the facile opportunity for 
it, because it is so readily unobserved. The standard 
examples we are about to quote from the books, will 
illustrate this. 

28. " In sifting a proposed Dilemma/' says Krug, 
"we are to look closely to the three 

Krug's rules for 

sifting Dilem- following particulars: — 1. Whether, in 
the Sumption,* the Consequent is a legi- 
timate inference from the Antecedent ; 2. Whether 
the Disjunction in the Consequent is complete ; 3. 
Whether, in the Subsumption,f the Disjunct Mem- 
bers are properly sublated. The following Dilemma 
is faulty in each of these respects. 

" If Philosophy be of any value, it must procure for us power, 
riches, or honor. 
" But it procures neither of them. Therefore," etc. 

" Here, 1, the inference is wrong, as Philosophy 
may be worth something, though it does 
not secure any of these external advan- 
tages; 2, the Disjunction is incomplete, as there are 
other goods, besides the three here enumerated; 
3, the Subsumption is false, as Philosophy has often 
been the means of procuring these very advantages." 

* Major premise. f Minor premise. 



6ec. III.] FALLACIES. 181 

29. Analogous to this is the old quibble to dis- 
prove the possibility of motion, which p uzzle a j, out 
also throws up the horns of a dilemma. Motlon ' 
Thus : 

" If Motion is possible, a body must move either in the place 
where it is, or in a place where it is not. 

" But a body cannot move in a place where it is ; and of course, 
it cannot move where it is not. 

" Therefore, motion is impossible." 

The Major Premise or Sumption is false and in- 
volves a Material Fallacy. The true 

■• . n • ,-, •, Solutioni 

statement is that, if motion is possible, 
a body must move from the place where it is to 
a place where it will be. This removes every ap- 
pearance of a puzzle. The Major Premise is false 
except with regard to one indivisible moment. But 
that is irrelevant to motion, which in its nature re- 
quires time, while the cognition of it supposes 
memory. 

30. To the same complexion comes the famous 

rid Puzzle named Ignava Ratio, i, e. the 

« , Ignava Eatio» 

argument for inaction, because events 

being predetermined or otherwise fixed, all effort to 

alter them, or to attain what is desirable and avert 

16 



182 LOGIC. [Chap. VL 

what is evil, is unavailing. Cicero thus states it as 
urged against calling in medical aid in sickness : 

" If it is fated that you shall recover from the present dis- 
ease, then you will recover whether you call in a physician or 
not. If it is fated that you shall not recover, then, with or 
without a physician, you will not recover. 

" But either the one or the other of these is fated. 

" Therefore, it will be of no use to call in a doctor." 

The obvious fallacy here, to look no deeper, lies 
in the fact, that the calling in of the doctor and 
using his prescriptions, may be the very means by 
which it is ordered that recovery shall take place; 
hence the first member of the sumption or major 
premise is false. And so of all analogous cases. 

31. The famous puzzle of Achilles and the tor- 
Achilles and the toise > which so lon g baffled the logi- 
tortoise. cians, aiming to prove, by logic, the 

logical absurdity, that the swiftest runner can never 
overtake the slowest, is put thus : 

" The swiftest runner can never overtake the slowest, if the 
latter has ever so little a start. Suppose, for instance, that 
Achilles runs ten times as fast as a tortoise, and that the tor- 
toise is one mile in advance at the outset. While Achilles is 
traversing this mile, the tortoise has advanced y^th of a mile 
farther ; before his pursuer has passed over this yoth, the tor- 
toise has advanced x^o tn ; an( ^ then, again, xoW^i an( ^ s0 on 



Sec. III.] FALLACIES. 183 

forever, always being some fraction, however small, of a mile in 
advance." 

The sophism here is disguised under a false state- 
ment of the problem. The real ques- The g op ] lislI1 
tion, when will Achilles overtake the ex Posed. 
tortoise ? is kept out of sight, and another wholly 
different substituted in its place, viz., if the 
tortoise is at any given point ahead of Achilles, 
how far will it have gone when Achilles shall reach 
that point ? This soon runs into infinitesmals which 
are practical zeros, and, even if theoretically infinite 
in number, really are all included in that finite length 
which Achilles will quickly get over, leaving the 
tortoise behind. 

32. Other puzzles abound on which we have no 

room to dwell. It is the less necessary, m , 

J 7 Such puzzles 

as a careful application of the principles have no chief 
already laid down, will readily solve pacem °s 10 ' 
them. The propounding and solution of such 
quibbles may be a casual diversion, it cannot be a 
principal object of pursuit, in any science worth 
serious study. 



CHAPTER VII. 

LOGICAL METHOD. 

1. Method, fieObdoz, is the way by which we pro- 
ceed to a given goal. Logical Method 

Method Defined. . ., n 1 . ,, • • i n 

is the way 01 applying the principles ot 

Logic to the discovery, confirmation, or elucidation 
of the truth. 

In order to this, it is necessary to determine 

the sphere and matter, the extension 

vision Defini- an( ^ intension, the objects and the qual- 

tion, and Rea- j^ies, with which we have to do. The 

soning. 

former is accomplished by Logical Divi- 
sion, and the latter by Definition, which have been 
duly treated in their respective places, in the Chap- 
ter on Conceptions. To this we refer the student 
as sufficient for present purposes, while we pass to 
consider more especially the use of Reasoning in 
the search and proof of truth. 

184 



Bee. I.] METHOD. 185 

2. It must not be forgotten that Logic does not 

give us the original facts, axioms, or „ . 

& . Lo s ic not tlie 

first principles, which constitute the Original source 

. . t i r of Knowledge. 

primary matter or groundwork of our 
knowledge. These are furnished by Its S(mrces enu . 
Intuition, either 1. Of the phenomena merated ' 
of consciousness, i. e, psychological facts : or 2. By 
sense-perceptions, i. e. of facts pertaining to the 
material and external world — or, 3. By supersensual 
intuitive truths, i. e. self-evident axioms : or finally, 
by testimony either spoken or recorded. _ _ , , _ 

* J * How Logic deals 

Logic deals with the matter thus af- with the matter 

/»-.-.. . nil iXii S0 famished. 

lorded in a two-iold way. 1. in the 
application of its principles to test and explicate 
what is contained implicitly in the matter so fur- 
nished by the intuitive faculties : 2. By guiding us 
in such use of our intuitive faculties, as shall be most 
effective for advancing our knowledge. According 
to the former, the laws of Conceptions, Judgments, 
and Reasonings show what is, and what is not, ne- 
cessarily implied by the facts and truths given us 
from other sources. In the latter, it helps to guide 
our inquiries, observations, and experiments towards 
the search for and intuition of such facts as will 
tend to elucidate or decide questions in issue, thus 

16* 



186 LOGIC. [Chap. VIL 

saving us the waste of our powers in irrelevant and 
fruitless investigations. 

Section I. — Original and Derivative Sources op 
Knowledge. 

3. Our Original Sources of Knowledge then are the 
Intuitive (including Self-Consciousness, 

Recapitulation v ° 

of sources of Sense-Perception, Self-Evident, Super- 
sensual truths), and Testimony. The 
Derivative are what we derive from them through 
the power of Discursive Thought, including Ab- 
straction, Generalization, Conception, Judgment, 
Reasoning. Some add to these Memory, 
of whom some class it with the former 
faculties, some with the latter. It is unnecessary to 
discuss this question here. It is enough that Me- 
mory is not itself a direct source of knowledge in- 
tuitive or discursive. It simply keeps and repro- 
duces what is known through the other faculties. 
Some questions too might arise, as to how far Testi- 
mony is an intuitive, or immediate source of know- 
ledge. It is not our plan here to go far in the 
discussion of such extra-logical questions. They 
are to be relegated to psychology, except so far as 
may be essential to a due understanding of Logic or 



Bee. I.] METHOD. 187 

its applications. It suffices for our present purpose 
that Memory, like the intuitive faculties, furnishes, 
inasmuch as it preserves, material for the discursive 
faculties, but is not itself discursive. 

4. Memory is an essential element in nearly all 
Testimony. It is rare that any one 

Memory in- 
bears witness simply to the cognitions volved in Testi- 

of the present moment. Almost all tes- y ' 

timony respects the past. 

5. Testimony is a fundamental source of know- 
ledge. All facts known to us beyond 3^^ of 
the narrow circle of our own experience, Testimony, 
must be learned from Testimony. And our gene- 
ralizations and reasonings would be extremely scanty 
for lack of material, without the results of the ex- 
perience of other men, added to our own, and au- 
thentically reported to us. 

Testimony may be either Oral, or Recorded iv 
historical writings, monuments, memen- q^ and Ke- 
toes, and tokens. The canons for dis- corded. 
tinguishing true testimony from false, and genuine 
from spurious, authentic from fictitious history, are 
manifold and easily accessible. To discuss them 
is aside of our present purpose and beyond our 
space. 



188 LOGIC. LChap. VIL 

6. There is, however, one species of testimony 
m , „ that is wholly unique, and above the 

Testimony of J . 

God in Ms Word plane of all human witnessing. We 
refer to the testimony of God in his 
Word. This is absolutely sure and infallible, be- 
ing the utterance of Him for whom it is impossible 
to err or to lie. It is the exclusive source and 
foundation of Christian Theology. It is absolutely 
true and authoritative. To unfold the rules for 
the correct interpretation of Scripture would be to 
trench on the sphere of exegetical theology. 

7. It is proper, however, to remark that the first 

principles of theology do not depend 
ed on the an- upon any process of reasoning, a priori 
orl y ° ° ■ or i n( l uc tive, but upon the authority of 
God who declares them. In a qualified sense, the 
true process for ascertaining what the Scriptures 
teach may be viewed as inductive. In other words, 
it simply ascertains and compares the actual teach- 
ings of Scripture, instead of deciding a priori what 
they may and may not teach. 

8. The application of the laws of thought or prin- 

ciples of logic to the facts, that are al- 
The laws of r # & ' 

thonght always ways coming before us in an isolated 
Bpp le ' and unorganized form, is constantly 



Sec. I.] METHOD. 189 

made, consciously or unconsciously, by all men. 
The power to do it is one of man's chief preroga- 
tives as compared with the brutes. To think at all 
is, either consciously or unawares, to conform to the 
laws of thought. All else called think- 

t Unlogical is 

ing only simulates and counterfeits it. counterfeit 
But, in proportion as this application oug 
of the principles of logic becomes comprehensive 
and complete, in regard to any given department 
of facts or truths, it becomes a scientific view of 
them. Thus, a comprehension of the facts con- 
cerning life, in their mutual relations, their har- 
mony and unity according to the necessary laws of 
thought, makes up the science of Physiology ; of 
the phenomena of the soul, Psychology ; of spatia) 
quantity and relations, Geometry. 

9. Science then is not a mere knowledge of die* 
jointed unreconciled facts or truths, but g c i eilce w h a tit 
a knowledge of these facts as mutually iSi 
related, harmonized, and unified, under all-inclu- 
sive principles and laws. But, in the sphere of 
actual being, of events or phenomena, To find ?flws ^ 
to ascertain their laws and principles is t0 ^ caTlses ' 
commonly to ascertain their causes. Towards this 
state all knowledge tends in proportion as it tends 



190 LOGIC. [Chap. VIL 

to perfection. And this, not only in each particu- 
lar department of inquiry considered 

Perfect know- 
ledge is scien- by itself, but in the relation of them all 

to each other. They are more and more 
comprehended in their mutual relations and har- 
mony, until they culminate in absolute unity in the 
Great First Cause, and the Infinite Mind. 

10. This process is actually going forward with 
All Sciences g reat rapidity as science advances. The 
tend to Unity, various Physical Sciences are more and 
more seen as distinct, yet cognate and harmonious, 
divisions of one great whole. The same is true of 
the various branches of Psychology and Metaphy- 
sics, in their mutual coherence and interdependence: 
while Physics have their deepest ground in Meta- 
physics, in the ideas of substance and cause, with- 
out which all being is a chimera, and all science a 

dream. So the several sciences, physical 

Scientia Scien- , . , . *. . ... 

tiarum! PMlo- and metaphysical, are constantly verging 
scphy and Onto- towards that scientia scientiarum, which 

logy. 

is at once the true Philosophy and the 
true Ontology. 

11. Philosophy and Science have been used very 
much interchangeably, and very much also in more 
or less contrast to each other. In the former case 



Sec. L] METHOD. 191 

they are used for that comprehensive view of facta 
and truths in the particular departments, 
or in the whole field of knowledge, above gd^ t^thei 
set forth. Thus we speak indifferently Compared and 

r J Defined. 

of the Science of Mind and of the Phi- 
losophy of Mind, of Natural Philosophy and Phy- 
sical Science. But the words are often used with a 
sort of contrast, according to which science is re- 
stricted to the domain of Physics, and Philosophy 
is more particularly referred to Metaphysics. This 
is especially so when these terms are used alone, 
without any qualifying adjunct. Thus, if we use 
the word Science alone and absolutely, we usually 
mean Physical Science. And when we speak of 
Philosophy absolutely and eminenter, we mean Me- 
taphysics, as including mind, which is the prime 
cause, and those first truths of Causality and Sub- 
stance, Time and Space, which variously condi- 
tion being, whether body or spirit. 

12. As all effective thinking, or application of the 
laws of thought, tends, and is indispen- 

i . ,-, j. j.* j? Logical Method 

sable, to the construction ot science, or inc i udes D e fi n i. 
thorough knowledge, so Logical Method tion » ^vision, 

and Reasoning. 

in every department of inquiry involves 

the three great logical processes which mutually 



192 LOGIC. [Chap. VII. 

supplement and complete each other. Definition, 
which unfolds the nature of the science according to 
its attributes or qualities : Division, which unfolds 
it according to its extension or the objects it includes : 
and Reasoning, in which we either guide our search 
for facts and truth, or interpret these facts by 
showing what can fairly be inferred from them. In 
regard to Definition and Division, it is unnecessary 
to expatiate upon them here. It is enough to refer 
the student to the principles already laid down on 
. these subjects. It is only necessary to 

Importance of J j j 

Definition and add, that exact Division and Definition 
are of the utmost moment to the suc- 
cessful investigation and treatment of any subject. 
We will now fix our attention on the application of 
the modes of reasoning to the discovery, elucidation, 
and proof of the truth, in regard to the object- 
matter so marked out by these processes. These rea- 
sonings are subject to different conditions, and have 
a different cogency and force, according as they are 
applied to Necessary or Contingent Matter. 
13. The former, as before defined, is that the 

a opposite of which the mind cannot con- 
Necessary and x x 

Contingent Dis- ceive without intellectual suicide. The 
latter is that whose existence is Con- 



Sec. II. j METHOD. 193 

tingent, and the supposition of whose non-existence 
involves no contradiction or absurdity. These two 
kinds of truth give rise to the two orders of reason- 
ing, respectively known as Demonstrative and Pro- 
bable, and to the three classes of Judgments classed 
by logicians respectively as, 

Sect. II. — Problematic, Assertory, and Apodictic 
Judgments. 

14. The two former apply to the region of Con- 
tingent,* the last to that of Necessary truth. This 
distinction in judgments concerns the degree of cer- 
tainty in the connection between the subject and 
the predicate. 

A. The Problematic Judgment is neither sub- 
jectively nor objectively certain : i. e. it 

J . . . Problematic 

is not certain to him who holds it, nor Judgment = 

can he enforce its acceptance upon P UU011 ' 

others. It is equivalent to mere opinion. 

B. Assertory Judgments are true and certain sub- 
jectively but not objectively, i. e. sure Assertory — 
to him who holds them, but incapable Fait k 

of being enforced on the acceptance of others of a 

* This must not, however, be pressed so far as to impugn the 
necessary existence of God. 

17 jj 



194 LOGIC. [Chap. VII. 

different moral disposition. Of this nature is belief 
or faith, especially Religious Faith. Its judgments 
are sure to the believer, although they cannot be 
enforced upon those of a contrary moral disposition. 
C. Apodictic or Demonstrative Judgments are 
subjectively and objectively sure : sure 

Apodictic Judg- . 

ments necessa- to him who holds them, and capable of 
y met being enforced upon all of sane mind, 

who can be made to understand them and the evi- 
dence for them. Of this nature are the truths in 
Mathematics, Logic, and some primary axioms in 
Ethics and Metaphysics. 

15. In regard to reasoning in the sphere of 
. m necessary truth or apodictic judgments, 

Reasoning from J x ° ° * 

Apodictic Judg- little need be said. The conclusions 

ments surei r> it • n i • t t 

ot all reasoning irom sucn judgments 

to others founded upon them, that conform to the 
principles of the syllogism in its various forms as 
set forth in formal logic, are as certain, and as im- 
possible to be false, as the premises. The 

Its power in the r , *, , « ■ ..11 .. 

Formal Sciences l° rma l sciences afford nne illustrations 
Illustrated by f the achievements of the logical faculty 

Geometry, 

in enlarging our knowledge, without 
in the least increasing its original materials, but by 
simply explicating them. The whole science of 



Sec. II.] METHOD. 195 

Geometry is but the logical unfolding of the con- 
tents of a few primary axioms. So also And ^ MathfU 
of the entire range of pure Mathematics, matics « 
and of pure Logic. All necessary and a priori 
truths, intuitive and deductive, afford premises for 
necessary conclusions. Thus, from the EeaS01lillg fTOm 
a priori truth that space is illimitable, a P riori t"^ 
it follows that it is immeasurable. From the a 
priori truth, " every event must have a cause," and 
the minor premise, " thunder has occurred" (or 
been an event), it follows that this 

From one a pri- 

thunder must have had a cause. Here on and one Con- 
the major premise is a necessary, the lngen P remlS6, 
minor a contingent but certainly proved truth ; 
and the conclusion is true, with a necessity condi- 
tioned on the truth of the minor, i. e. in this sense, 
with a conditional necessity. In genuine logical 
reasoning the conclusion is a necessary consequence 
of the premises. In proportion then as they are 
necessarily true, the conclusion is so likewise^ 1 a 
this we have the type of all purely 



196 LOGIC. [Chap. VII. 

Sect. III. — Deductive Keasoning. 

16. This has place in all cases of Reasoning 
'\ B from wholes known in whatever way, 

This the type of ^ . 

Deductive Rea- whether of Extension or Intension, to 
the parts included under them; from 
Genus to Species, and individuals under them, or 
from the marks of the individual or species to the 
marks of those marks. So far as we have any- 
generic truths, propositions or judgments established, 
whether in necessary or contingent matter, these 
furnish premises whence we can reason with neces- 
sary certainty, to individuals or classes contained 
under them. If it be established that, 
(Intensive Syllogism) — " Polyps are animals, 

And that 

Animals have sensation, 

then it follows of necessity that 

Polyps have sensation." 

Deductive Reasoning then is from Generals to 
Deductive Rea- Particulars — the form, as we shall see, 
Boning is from of near] al} demonstrative and abso 

Generals to Par- J 

ticulars. lutely conclusive reasoning. 

17. But how do we obtain these universal or 



Sec. IV.] METHOD. 197 

Generic Judgments in Contingent Mattel, when all 

that we know originally of mind is 

the individual facts that come under (j enera i j u ^ g . 

the purview of consciousness, and of ments ** Con " 

tingent Matter7 

matter, what are cognized through our 
senses? facts too, the opposite of which are pos- 
sible, and which it is conceivable might not be re- 
peated beyond the sphere of experience thus far 
had ? From the fact that such persons as we have 
known die, how do we reach the conclusion that all 
men are mortal ? From the fact that some water 
is composed of oxygen and hydrogen, how do we 
know that all water is so constituted? This brings 
us to reasoning from particular facts to a general 
law 01 truth, which is, 

Sect. IV. — Induction. 
17. This is the principal instrument of scientific 
progress, and of all advance in human 

i By Induction, or 

knowledge, except through Divine Re- reasoning fr^ 

i ,. .,i • ,i -i r» i Individuals to 

velaiion, witnm the realms of actual &enera 
being. For this is a region of facts, Actual beings 
objects, phenomena of actual existence are Lldivi ^ als - 
which are first known as individuals, and might or 

might not be, according to the good pleasure of God. 
17* 



198 LOGIC. [Chap. VIL 

The Formal Sciences and Metaphysics do not of 
Scope of Formal themselves discover or prove any actual 
Sciences. being. They only show certain neces- 

sary conditions or consequences of any facts of actual 
being, which may be brought to light by the other 
cognitive powers. 

But all advance in the knowledge, and especially 
the scientific knowledge of actual being, 

All progress in ° 7 

Scientific Know- is by ascent from particular facts to 
SglsToi g eneral laws - Xt proceeds therefore, 

Individuals to from what we know in some cases, to 
Classes. . 

inter that the like is true in all similar 

cases. This is induction or inductive generalization. 

T Induction, however, is more than Gen- 

Indnction more 7 7 

than General!- eralization, which it always includes. 
There may be generalization without 
induction, though there can be no induction without 
generalization. Generalization combines in a class 
objects having similar qualities, and denotes them 
In what respect by a class-name. Induction concludes 
it is so. from the fact that some of a given class 

already generalized possess some given property, all 
others of that class possess it — in other words, that 
because a certain mark A is, in some cases, attended 
with a certain mark B ; it is so in all other cases. 



Sec. 1V.J METHOD. 199 

Thus, from the fact that some fire tortures living 
flesh in contact with it, we reason in- 
ductively that all fire will do it. Here 
is generalization in this way, and to this extent, that 
what is found true of some, is extended to all, that 
have a given mark. 

18. The great question then, in regard to this 
class of cases, which needs to be deter- 

The great qu.es- 

mined, is, when are we warranted in tion regarding 
taking some instances that have come nc 10IL 
under our knowledge, as samples or accurate repre- 
sentatives of a whole class, including;, it 

7 & ' What are tests 

may be, like cases innumerable ? What or crucial in- 
are the criteria which distinguish these 
crucial instances from others which warrant no 
such inference ? 

19. There is the test of a complete enumeration 
of all the instances or individual cases simple Bnn- 
composing the class in question. If aeration. 
these all, without exception, have the property in 
question, then it of course belongs to the whale 
class. Thus, if the season of greatest 

growth is in May, June, July, August, 
which are the only months whose names are with- 
out the letter r, then the general conclusion follows 



200 LOGIC. [Chap. VII 

with absolute certainty, that the months without 
the letter r are those of greatest growth. If it has 
been found from actual observation, that each of 
the planets moves in an elliptical orbit, then it is 
true beyond a peradventure, that all the planets 
move in such orbits. This is what Bacon called 
Induction per simplicem enumerationem, by the mere 
enumeration of all the cases involved. 

Why this is Em- 
pirical Indue- It has also been named Empirical In- 
duction, because its compass is limited 
to actual experience, and it detects no cause and 

Andnnimport- establishes G0 la ^ reaching beyond 
ant. such experience. It is therefore com- 

paratively unimportant. That induction alone is 
Ih onl fruit- fr^ftd which enables us to go beyond 
ful Induction. suc h cases as have fallen within our 
experience, to an indefinite number of like cases, 
i. e. all of the same class not yet brought within 
the range of our experience. 

20. In order to this, it is necessary to ascertain, 

Requisites to it. not onl 7 the empirical fact, that, in 

A Causal such instances as have fallen under our 

Agency, cognizance, the phenomenon in question 

has occurred, but that there is a causal agency, or 

other uniform concomitant, connected with them 



Pec. IV.] METHOD. 201 

which ensures it, and which attends all like instances, 
Then, when it is settled what is the cause or mark 
of any given phenomenon, the principle that like 
causes produce like effects, which is either self-evi- 
dent, or so nearly so that all mankind act upon it, 
induces the conclusion that, in all similar cases, we 
may anticipate a like phenomenon. 

21. The difference between such an induction 

and that which is purely empirical, per 

7 . ,. .,.-,.! Difference from 

simplieem enumerationem, is strikingly gi le Enmne- 

illustrated in the second example of the rafci(m nitra- 
ted. 
latter kind, above given, which was the 

inductive conclusion that all the planets move in 

elliptical orbits, from observing that each of them 

moves in such orbits. This, however, of itself, 

creates only a moderate presumption, that any 

planets now unknown and yet to be discovered, 

move in such orbits. But when it was ascertained 

that the Centripetal and Centrifugal 0aTlsal Force 

Forces act jointly on all the planets, and Discovered. 

that the product of this joint action is an elliptical 

orbit, then the conclusion was indisputable, that all 

planets observed and unobserved, move in elliptical 

orbits. 

22. What then are the Tests of such Causal 



202 LOGIC. [Chap. VII. 

Agency, or other equivalent concomitant, and proof 

Tests of Causal of a g iven phenomenon? The proofs 
Agency; et<? ^hat a gi ven object or agency is, or con- 
tains in itself, the cause, or invariable concomitant of 
a given effect, so that we are warranted in asserting 
that the instances observed are as good as the entire 
Inductive Syllo- class of like instances? The Inductive 
^ m ' Syllogism naturally falls into the Third 

Figure. Thus : 

"XYZ have polarity, 
X Y Z are (represent quoad hoc) all magnets, 
■\ All magnets have polarity." 

It may, however, be put more awkwardly, in the 
First Figure. Thus: 

"XYZ have polarity, 
All magnets are (represented quoad hoc by) XYZ. 
.*. All magnets have polarity." 

In either case the question is, when do the parti- 
The Question re- cular cases X Y Z so represent the 
garding it. whole class, or when are they so proved 
to be, or *>o contain the causes or uniform con- 
comitants of a given phenomenon, that they fairly 
represent the whole class, and warrant a universal 
inductive conclusion ? 



Bee. IV.] METHOD. 203 

1st Criterion, the Method op Agreement, 
—If, whenever a given object or agency m ^ ^ ^ 
is present, without counteracting forces, Method of 
a given effect is produced, there is ^ e 
strong evidence that we have found the true cause 
of the effect, which will always produce it, in tho 
absence of counteracting forces. Thus, 
if, in all cases of the application of 
given degrees of heat, clay hardens, lead melts, and 
water boils, it is just to conclude that this is the 
real cause of these phenomena, and that whenever 
it is applied in such measure to these several sub- 
stances, they will re-occur. It is to be borne in mind, 
however, that the same effect may pro- 
ceed from different causes. In order to B^Stmay 

determine to which of two possible P roceed from 

different causes, 

causes it is due, in any given cases, the 
distinctive indications of each respectively must 
be sought. This is usually not difficult. The 
sensation of heat may arise from the general warmth 
of the weather, from an artificial fire, from exces- 
sive clothing, or from fever. It is usually easy, in 
view of all the circumstances, to determine which, 
But if not, unreal causes may be eliminated by the 
2d Criterion ; the Method of Difference; 



204 LOGIC. [Chap. VII. 

— This is given when, the supposed cause being 
present the effect is present, and this 
thod of differ- being absent the effect is wanting, i. e. 
unless in the latter case other coun- 
xcep ion. ter-agents are present to neutralize it, 
or in the former to produce it. Thus, it is double 
proof that sound is the result of vibra- 
tions of air excited by the resonant 
body, if, on the one hand, whenever sound is heard, 
such vibrations are found; whenever such vibra- 
tions appear sound is given forth ; and if, on the 
other hand, a bell or other sonorous body, suspended 
and struck in an exhausted receiver, yields no sound. 
It proves that the contact of moisture is the cause 
of the decomposition of animal matter, if, whenever 
the latter occurs such moisture is present ; if dry- 
ness checks or arrests it ; and if salt, which prevents 
it, acts by detaching the water from the meats which 
it preserves. If, when reason is present, there is 
accountability, and when it is absent there is none, 
then it is a condition of accountability. 

3d Criterion — accounting for residual varia- 
tions without invalidating; the proof of 

8dTest, Besid- 

nal variations the supposed cause. Thus, it was found 

iooonnted&r. ^ gound traveled f aster than what 



Bee. IV.] METHOD. 205 

seemed the true theory of its law of velocity allowed. 
It was suspected, however, that the rarefaction of 
the air, arising from the heat produced by the mo- 
tion of the sound, accelerated its progress to this ex- 
tent. Experiments proved this conjecture true, 
and thus confirmed the original hypothesis.* 

* The following striking example is given in the words of 
Hkomson'a Laics of nought, !New York Edition, pp. 262-3, Chap. 
VII. 

" In Sir Humphrey Davy's experiments upon the decomposition 
of water by galvanism, it was found that besides the two compo- 
nents of water, oxygen and hydrogen, an acid and an alkali were 
developed at the two opposite poles of the machine. As the 
theory of the analysis of water did not give reason to expect 
these products, they were a residual phenomenon, the cause of 
which was still to be found. Some chemists thought that elec- 
tricity had the power of producing these substances of itself: and 
if their erroneous conjecture had been adopted, succeeding re- 
searches would have gone upon a false scent, considering galvanic 
electricity as a producing rather than a decomposing force. The 
happier insight of Davy conjectured that there might be some 
hidden cause of this portion of the effect: the glass vessel con- 
taining the water might suffer partial decomposition, or some 
foreign matter might be mingled with the water, and the acid 
and alkali be disengaged from it, so that the water would have 
no share in their production. Assuming this he proceeded to try 
whether the total removal of the cause would destroy the effect, 
or at least the diminution of it cause a corresponding change in 
the amount of effect produced. By the substitution of gold vessels 
for the glass without any change in the effect, he at once deter- 
18 



206 LOGIC. [Chap. VII 

4th Criterion. Concomitant Variations.— 
, , m „ If, as the amount of the supposed causa 

4th Test. Con- ^ . 

comitant Varia- varies, the effect varies proportionally, 
it is strong evidence of its being the 
real cause. " That the column of mercury in the 
Torricellian tube was counterpoised by a column 
of air, was proved by Pascal when he caused thb 
instrument to be carried up the mountain, and 
found that as the ascent gradually diminished the 
height of the column of air above it, so was the 
column of mercury it was able to sustain diminished 
in proportion." 

mined that the glass was not the cause. Employing distilled 
water he found a marked diminution of the quantity of acid and 
alkali evolved; still there was enough to show that the cause, 
whatever it was, was still in operation. Impurity of the water 
then was not the sole, but a concurrent cause. He now conceived 
that the perspiration from the hands touching the instruments 
might affect the case, as it would contain common salt, and an 
acid and an alkali would result from its decomposition under the 
agency of electricity. By carefully avoiding such contact, he 
reduced the quantity of the products still further, until no more 
than slight traces of them were perceptible. What remained of 
the effect might be traceable to impurities of the atmosphere, de» 
composed by contact with the electrical apparatus. An experi- 
ment determined this ; the machine was placed under an ex- 
hausted receiver, and when thus secured from atmospheric 
influence, it no longer evolved the acid and the alkali." 



Sec. V.] METHOD. 207 

When either of these criteria is found, free from 
conflicting evidence, and especially when several of 
them concur, the evidence is clear that the cases 
observed, are fair representatives of the whole class, 
and warrant a valid universal inductive conclusion. 

Sect. V. — Hypothesis. 
23. But why make observations and experiments 
in one direction, or for the purpose of Reason for Hy. 
testing one view of the cause of given pothesis. 
phenomena, rather than any other ? It can only be 
because the mind entertains some conjecture or sus- 
picion that this may correspond wit! the facte. 
Thus it is led to institute investigations 
and trials for the purpose of testing the ^Se'conjeT 
truth of this conjecture. Such a con' toe or Tenta - 

tive Theory. 

jecture so entertained is a Scientific Hy- 
pothesis, which is thus but a provisional and tentative 
theory, while a true theory is a proved hypothesis. 
Such hypotheses, although they have often been 
abused, by the premature or unwarrantable assump- 
tion of their truth, are indispensable to effective 
progress in science. Without such a „ 

1 ° Use and Neaoa- 

guide and stimulus, all observations and sity of Hypo, 
experiments would be aimless, and com- 



208 LOGIC. [Chap. VU 

monly fruitless. Indeed, for the most part, they 
would be unattempted. Investigations so guided 
have led to nearly all the great achievements of 
scientific progress. 

24. Some confound Theory with Hypothesis, and 
„ « r™ accurate writers often find it difficult to 

How far Theory 

and Hypothesis use them so as to avoid all shades of 

are synonymous. . ^ , ±1 

synonymous meaning, .but neverthe- 
less, correct use points towards the difference we have 
indicated. Hypothesis could not be well substituted 
for Theory, when we speak of Wells' theory of dew, 
or Dalton's theory of definite chemical proportions, 
or the Newtonian theory of universal gravitation. 
And yet theory is often used for hypothesis, L e. 
for an unproved doctrine or speculation, or a tenta- 
tive and provisional, but uncertain explanation of 
phenomena. Thus we speak of Smith's Theory of 
the Moral Sentiments ; the exploded phlogiston and 
anti-phlogiston theories. Some use theory for a 
provisional and unproved explanation of a large 
group of facts. This however is but an hypothesis 
regarding such a group of facts. 
~ n ... n In regard to the distinction be- 

Definition of fe 

some Scientific tween Theoretical and Practical Judg- 

Terms. 

Judgments. ments, and other Scientific Terms, we 



Sec. V.] METHOD. 209 

quote the following from Thomson's Laws of 
Thought: 

" Judgments that relate to speculation only, are 
called Theoretical : those which refer to x , 

Judgments The- 

practice are Practical. Judgments oretical, Practi- 

,, . . t ., n n cal, Demonstra- 

tliat require or admit of proof, are ble> JjlAamam 
called Demonstrable; those which are stral)le ' 
manifest from the very terms, are Indemonstrable*. 
Thus much being premised we can define certain 
subordinate parts of a science. 

An Axiom is an indemonstrable theoretical judg- 
ment. A Postulate is an indemonstra- Axiom p ostu . 
ble practical judgment. A Theorem is late, Theorem. 
a demonstrable theoretical judgment. 
A Problem is a demonstrable practical 
judgment. A Thesis is a judgment Thesis. 
proposed for discussion and proof (but with Aris- 
totle it sometimes means an axiom of some special 
science or disputation). An Hypothesis 
is a judgment provisionally accepted as 
an explanation of some group of facts, and is liable 
to be discarded if it is found inconsistent with them. 
A judgment which follows immediately from an- 
other, is sometimes called a Corollary 
or Consectary. One which does not 

18* 



210 LOGIC. [Chap. VIL 

properly belong to the science in which it appears, 
but is taken from another, is called a Lemma. One 
Lemma. which illustrates the science where it ap- 

Scholion. pears Hut is not an integral part of it is 

a Scholion." 

25. The great distinction of Scientific Genius lies 
Chief mark of chiefly in this insight which, with keen 
Scientific genius, discernment of analogies, anticipates the 
truths or laws of nature, and devises observations 
and experiments to prove or disprove them. So 
Newton suspected that the same force which causes 
the falling of an apple, propels all matter, and pro- 
duces the revolution of the planets; Franklin, 
that lightning is a discharge of electricity. They 
proceeded to verify these hypotheses by experiments 
and observations which proved them. While the 
legitimate use of hypothesis is thus advantageous 
and essential to science, the cautions needful to be 
observed to prevent the abuse of it are, 
Cautions in Re- A. No hypothesis should be assumed 
S* r • t( \ ™°\ to account for what can be otherwise 

thesis. 1. Must 

be needed. accounted for, on existing and known 
principles. 

B. It should be adequate to account 

2. Adequate. ^,11 • j- 

for the phenomena in question. 



Sec. VI.] METHOD. 211 

C. The facts to be accounted for should be real 

and not imaginary, as the question be- „ mi . 

# & J } ^ 3. The facts to 

fore mentioned of Charles II. to the be explained 

-r> ici«j_ i i • n i • ± must be reali 

Koyal feociety, why a live nsn in water 
would increase its weight, while a dead fish wo aid 
not, and quite perplexed some of its members, until 
it occurred to them to inquire if the fact were so. 

D. It should be independent of ^Subsidiary 
subsidiary hypotheses — it should not H yP otneses - 
require other hypotheses to account for itself. 

E. It should not be assumed to be To be accepted 
true until proved to be so. wliei1 proved. 



Sect. VI. — Analogy. 

26. When it is argued from a known resemblance 
between objects or classes in some known B eason i n g f rom 
particulars, that they resemble each Analogy defined. 
other in other respects, this is reasoning from 
analogy. It has been common to define analogy as 
a proportion between objects. When 
we reason that because men resemble 
animals in having life and sensation, they therefore 
resemble them in the power of locomotion, or in 
the grade of their intelligence, we reason fro*xi 



212 LOGIC. [Chap. VIl k 

analogy, or the relative proportion of objects.* It 
is obvious that this is a very uncertain argument, 

Has only a pro- an( ^ can > in no case > r * se higher than 
bable force. mere probability. This probability will 

be weaker or stronger according to circumstances. 
The argument for future retribution, from the pre- 
sent evils visited upon sin, is certainly stronger than 
the argument that brutes have reason because other 
conscious beings have it. But in neither case is it 
conclusive. The argument from analogy may be 
well employed to add a cumulative 

Jttay strengthen * J 

other argu- force to other arguments. It is not, 

ments. -, • -. . n • . -, •» 

however, in any case conclusive of itseli. 
27. Its most important service, however, is in 
Most useful in refutation of fallacious arguments. It 
refutation. often has in this way a powerful nega- 
tive force. Thus, if it be objected to the doctrine 
of future punishment that the infliction 
of pain is inconsistent with the benevo- 
lence of God, this argument is refuted by the fact 

* To reason from Analogy, is to reason from the Intension ol 
that to which it relates. To reason by Induction is to reason 
in extension from one or some objects in a class to all in that 
class. In analogical reasoning, we argue from a resemblance m 
Borne qualities to a resemblance in other qualities. 



Examples. 



Sec. VII.] METHOD. 213 

that God does inflict pain, or so order and permit 
events that it is undeniably inflicted, in this life. 
The alleged impossibility of the future life and 
immortality of the body on account of its death, is 
disproved by the fact that in all nature life is 
evolved from death, and the seed which we sew 
u is not quickened except it die." 1 Cor. xv. 36. 

Sect. VII. — Categories. 
28. These are summa genera of predicables. 
Logicians and metaphysicians have Definition of 

SOUght to give complete lists of these Categories. 

summa genera, to which all particular predicables 
and classes of predicables might be referred. It 
has, however, been hard to find any such exhaus- 
tive enumeration. Says Whateley, " The Categories 
enumerated by Aristotle, are obaia, Artie's Cate- 
nbaov, tzoIov, npoozt, nod, ndre, xzladat, g° rieSi 
eyeiv, noiztv, 7i6.oyjz.iv) which are usually rendered, 
as adequately as, perhaps, they can be in our lan- 
guage, substance, quantity, quality, relation, place, 
time, situation, possession, action, suffering. The 
catalogue (which certainly is but a very crude one) 
has been by some writers enlarged, as it is evident 
may easily be done by subdividing some of the 



211 LOGIC. [Chap. VIL 

heads ; and by others curtailed, as it is no less evi- 
dent that all may ultimately be referred to the two 
neads of substance, and attribute, or (in the language 
of some logicians) accident." Some, however, per- 
haps justly, translate e%eiv, " mode of action," in- 
stead of "possession." Aristotle's Categories are 
rather metaphysical than logical. 

29. Kant's celebrated four triplets of Categories 
Kant's Oate- are certainly ingenious, and, if not ab- 
gories. solutely exhaustive, in a metaphysical 

view, go far to show the nature and a priori basis 
of the several logical judgments. According to 
him all judgments must connect the predicate with 
the subject so as to involve under the head of, 

1. Quantity. 2. Quality. 3. Relation. 4. Modality. 

Unity, Affirmation, Substance and Accident, Possibility, 

Plurality, Negation, Cause and Effect, Reality, 

Totality. Limitation. Action and Reaction. Necessity. 

It may be observed that the first of these triplets 
corresponds to Singular, Particular, and Universal 
Judgments; the second to Affirmative, Negative, 
and Restrictive* Judgments; the third to Categori- 

* Restrictive Judgments "are such as contain a negative in the 
predicate-conception, e. g., God is infinite. The human soul is 
immortal. In respect to their contents, they are negative ; but 



Sec. VII.] METHOD. 216 

cal, Conditional, and Disjunctive Judgments; the 
fourth to Problematic, Assertory, and Apodictic 
Judgments. 

30. Tables of Categories are almost as various 
as the writers on Logic and Metaphy- 
sics. McCosh gives the following as 

a provisional summary of primary judgments. 

1. Identity and Difference. 5. Quantity. 

2. Whole and Parts. 6. Eesemblance. 

3. Space. 7. Active Property. 

4. Time. 8. Cause and Effect. 

31. J. S. Mill in his Logic gives the following 
classification of nameable things in 

the spirit of the Positive Philosophy. 

1. Feelings or states of consciousness. 

2. The minds which experience these feelings. 

3. The bodies or external objects which excite certain of 
these feelings, together with the power or properties whereby 
the/ excite them. 

in respect to form, they are affirmative. Logically considered, 
therefore, they belong to the class of affirmative judgments. 
These judgments are also called infinite, or more properly indefi- 
nite, because, by means of a predicate involving a negative, the 
subject is transferred from the sphere of definite conception to 
that of indefinite conception, a sphere to which it does not pro- 
perly belong." — Gerharfs Philosophy and Logic, p. 214. 



216 



LOGIC. 



[Chap. VII 



4. The successions and coexistences, the likenesses and un- 
likenesses between feelings and states of consciousness."— 
LygiCy I. 111. 

32. Thomson (Laws of Thought, p. 315) just 
attempts the following : 



TABLE OF THE CATEGORIES. 



1 



Substance 



Attribute 



Quantity 



Quality 



Relation 



" of Time 

of Space 

of Causation 

of Composition 

of Agreement and Repug- 
nance 

of Polar Opposition 
, of Finite to Infinite. 



Bee. VIIL] METHOD. 217 



Sect. VIII. — Harmony and Co-ordination op Sciences 

33. As the application of scientific method to any 
given and mutually related set of phenomena or 
truths develops a science of these facts, like the 
Science of Botany, Anatomy, Ethics, etc., so many 
of these sciences are related to each other as Genus 
and Species. Thus Ornithology, Piscatology, etc., 
under Zoology. Various attempts have 

, t i •*» j-i n • Classification 

been made to classify the sciences so and Mutual 
as to show their Mutual Harmony and Harmony of 

the Sciences. 

Interdependence. It is plain that they 
might be logically divided and sub-divided from 
various stand-points, which have been taken ac- 
cording to the respective aims and purposes of the 
authors. Thus they may be divided into the 
Speculative and Practical, or the Phy- speculative and 
sical and Metaphysical, or the Formal Practical, etc. 
and Material, etc., with their respective subdivisions. 
Attempts of this sort have often been made, with 
considerable success and utility. 

34. Compte and the positive school of philoso- 
phers, however, amidst their enormous errors, have 
unfolded a scheme of classification and co-ordination 
among the sciences, at once beautiful and fruitful, 

19 



218 LOGIC. [Chap. VIL 

which has commanded wide acceptance among those 
who have attended to the subject. 

Starting with Descartes' suggestion, that the 
order of arranging the sciences should be from the 
simplest to the more complex, he adopts the fol- 
lowing, which at once commends itself by its sim- 
plicity, naturalness, and beauty, and which we give, 
as we find it, in a form most available for our pre- 
sent purpose, in Thomson's Laws of Thought, pp. 
316-19. 

" Mathematics, or the science of quantity, is at 
once the most simple in its elements and the most 
general in its application, entering more or less into 
all the sciences of nature, and constituting almost 
the whole of that which comes next it in the order 
of dependence. Astronomy, or the science of the 
heavenly bodies, is the application of mathematical 
truths to the laws of matter and motion ; matter and 
the motions of material bodies being the new con- 
ception which belong to this science. Physics, being 
the science, or rather group of sciences, which is 
conversant with the general laws of the world, so 
far as they relate to beings without life or organiza- 
tion, would come next ; and it imports, in addition 
to the conceptions of Astronomy, those of light, of 



Sec. VIII.] METHOD, 219 

heat, of sound, of electricity, of magnetism, and 
many others. Chemistry would rank next, which 
is the science of the decomposition and combinations 
of the various substances that compose and surround 
the earth. Next in order of complexity would rank 
Physiology, founded on the additional conception 
of vegetable and animal life. To this would suc- 
ceed Anthropology, or the science of man's nature; 
and to this Social Science, which ascertains the laws 
that govern men when combined in cities and na- 
tions. Each of these departments may be divided 
into many branches; as Physics into Acoustics, 
Optics, Electricity, and the like ; or Social Science 
into Morals, Politics, Political Economy, Law, and 
the like. 

" On comparing scientific works, differences in the 
mode of teaching the same subject become appar- 
ent. In one the pure theory of Astronomy is 
presented; in another the striking features of its 
historical progress as a science, with speculations on 
the historical sequence of the phenomena themselves ; 
in a third the practical applications of which the 
science admits in respect to the comfort and progress 
of mankind. This threefold mode of treatment 
runs through all the sciences ; and in a table of 



220 LOGia [Chap. VII. 

them might well be expressed. The classification 
would thus embody all that is valuable of another 
system of classes, that according to the purpose 
towards which the science was directed. 

"A classification which advances on Descartes' 
principle, from the more simple to the more com- 
plex subjects, which commences from the notions of 
extension and quantity, and proceeds through ma- 
terial things, up to living, intelligent, and moral 
agents, ought to coincide with the order in which 
the sciences themselves have reached maturity. 
And this it certainly does. Mathematics had made 
good its ground when astronomy was yet in its 
infancy; physics began to obtain a sure footing 
later than either; whilst the sciences which relate to 
life are still very immature; and some of the main 
problems of social science are yet matter of contro- 
versy even in our own days. 

" There is besides a general correspondence between 
this classification and the order in which the various 
objects of science came into being. The heavenly 
bodies were first appointed their paths in the celes- 
tial spaces; then the surface of our earth was pre- 
pared for living creatures ; then they were created 
after their kind, and man the last. The social life 



Sec. VIII.] 



METHOD. 



221 



of man grew up last of all, when his race was mul- 
tiplied on the globe ; and ever as new elements ap- 
pear, the conditions of society are being modified 
even to the present time." 
Hence emerges the following 



"classification of the sciences. 

Group. Mode of Treatment 

I. Mathematics Theoretical. Historical. Applied 

II. Astronomy Theoretical. Historical. Applied. 

III. Physics Theoretical. Historical. Applied. 

IV. Chemistry Theoretical. Historical. Applied. 

V. Physiology Theoretical. Historical. Applied. 

VI. Anthropology.... Theoretical. Historical. Applied. 
VII. Social Science Theoretical. Historical. Applied. 

V , 1 

Beugious Philosophy." 
19* 



APPENDIX. 



APPENDIX A. 

EXAMPLES FOR PRAXIS. 

The following examples may be used for practical exercise in 
Conceptions, Judgments, and Reasonings of all kinds. In 
analyzing Syllogisms, let the student complete them when un* 
finished, and point out their kind, whether Categorical o1 
Hypothetical; if the former, give their Mood and Figure; if 
the latter, show whether they are Conditionals, Disjunctives, or 
Dilemmas. Mark the Enthymemes, Sorites, Prosyllogisms, 
and Episyllogisms. In all cases show whether the. Syllogism 
is valid or invalid, and if invalid, indicate the kind of Fal- 
lacy. 

1. Body is extended substance, 

This inkstand is a body, 
•\ It is extended substance. 

2* Plants are bodies with organization, 
Potatoes are plants. 



22? 



224 APPENDIX. 

3. Animals are bodies having organization and sensation, 
Frogs have organization and sensation. 

4. Bodies having organization, sensibility, and reason are 

men, 
The poets are men. 



5. X Y Z> are ruminant, 

X Y Z, are (as good as) all horned cattle. 

6. Quadrupeds are animals, 
Worms are animals. 

7. Oaks are vegetable, 
Oysters are not oaks. 

8. Beasts are animals, 
Birds are not beasts. 

• . •••••«... 

9. These emigrants are either Scotch, Irish, or German, 
They are not Germans. 

10 These people are patriots because they are free. 

11, If the classics teach how to produce wealth they ought 
to be studied, 
They do not so teach. 



• • ••••••••* 



EXAMPLES FOR PRAXIS. 225 

12. If we can prevent what occurs we ought not to fret 

about it, 
If we cannot prevent what occurs we ought not to fri* 

about it, 
But either we can or cannot prevent it. 

13. A Christian nation is brave, 
A brave nation is free, 

A free nation is happy. 

14. A plane triangle is a rectilineal figure having three sides, 
A plane triangle is A B C. 

15. All these trees make a thick shade, 
This catalpa is one of these trees, 

.*. It makes a thick shade. 

16. Whatever study gives knowledge relative to either of 

the three learned professions ought to be a part of 
liberal education ; 
Geology and Mathematics do not give such knowledge, 
.'. They ought not to be studied. 

17. If all men are liars then nothing can be proved by 

human testimony ; 
But some things can be proved by human testimony, 
.*. No men are liars. 

18. Typhoid fever is epidemic, 
Because A. B. and C. have it. 

r 



226 APPENDIX. 

19. An inflated currency promotes national prosperity, be* 

cause it enables persons to make rapid fortunes. 

20. What we eat grows in the fields or is the flesh of animals, 
Cooked food is what we eat, 

.'. Cooked food grows in the fields or is the flesh of animala. 

21. The rumor that A. B. has committed a given crime is 

universal, for I heard it from Mr. A and Mr. B. 

22. If we say the Baptism of John was from heaven we con- 

demn ourselves for not believing him ; 
If we say it was of men, the people will stone us ; 
But we must, if we say any thing, confess it was from 

heaven or of men ; 
•*• If we say any thing, we must either condemn ourselves, 

or the people will stone us. Luke xx. 4-6. 

23. Some flowers are (all the) tulips, 
All flowers are beautiful, 

.', All the tulips are beautiful. 

24. All false religions have sustained their claims by alleged 

miracles, 
Christianity sustains its claims by alleged miracles ; 
,'. It is a false religion. 

25. The minute-hand can never overtake the hour-hand of a 
clock, because while it is passing to the point where the hour- 
hand is at any given moment, the latter will have advanced 



EXAMPLES FOE PRAXIS. 227 

some distance : and when the former has passed over this dis- 
tance the hour-hand will have advanced still further; and 
bo on ad infinitum. 

26. This man has an excellent character because he belongs to 
an excellent church, as appears from its being composed 0/ 
such excellent men. 

27. He who is most hungry eats most, 
He who eats least is most hungry, 

•\ He who eats least eats most. 

28. If the taking of an oath to discharge our duty tends ki 
secure its performance, then it ought to be repeated in refer- 
ence to every duty of life ; if it does not, then the civil oa-ths 
administered are superfluous. But one or the other of these 
is true. .*. The oaths commonly administered are superfluous, 
or they should be repeated in connection with every duty of 
life. 

29. No man is rich who is not content, 

No miser is content (t\ e. every miser is one who ib uot 
content), 
■', No miser is rich. 

30. Men can live without animal food, and they can live 

without vegetable food, as has been often demonstrated, 
But all food is either animal or vegetable, 
.'. Men can live without food. 

31. He who calls you a man speaks truly, 
He who calls you a fool calls you a man, 

V. He who calls you a fool speaks truly. 



228 APPENDIX. 

32. Useful studies ought to be encouraged, 

Logic, since it helps us to reason accurately, is such, 
.'. It ought to be encouraged. 

33. X Y Z have polarity, 

X Y Z are (as good as) all magnets, 
for polarity appears wherever magnets are ; it disappears when 
they are withdrawn, unless other polar forces are present, and 
it increases with the power of the magnet ; 
.*. All magnets have polarity. 

34. Some men of genius are (all) the poets, 
Some poets are melancholy. 



35. The mind is a thinking substance, 
A thinking substance is a spirit, 

A spirit has no composition of parts, 

That which has no composition of parts is indissoluble, 

That which is indissoluble is immortal, 

Therefore the mind is immortal. 

36. Protagoras engaged to teach Euathlus the art of pleading 
for a large reward, one half to be paid at once, the other half 
when the latter should have gained his first cause in court. 
After a short time Protagoras sued Euathlus for the unpaid 
moiety, enforcing his claim by the following Dilemma : 

If the case is decided in my favor, the sum will be due 
to me according to the finding of the court ; 

If it is decided in your favor, the sum will be due to me 
according to our contract, 



EXAMPLES FOR PRAXIS. 229 

But it must be decided either in my favor or yours. 
••. Whether I gain or lose the cause I shall be entitled to 

the reward. * 
Euathlus thus answered . 
If I gain the cause, nothing will be due you according to 

the decision of the court, 
If I lose it nothing will be due you according to oui 

contract ; 
But I shall either gain or lose it, 
.\ In neither case shall I pay you the reward. 

37. A policy which promotes the national wealth ought to 

be adopted ; 
But the education of the people increases their wants 
and expenditures, and therefore does not increase 
national wealth ; 
■\ It ought not to be adopted. 

38. All is not gold that glitters, 
Tinsel glitters, 

,\ It is not gold. 

39. If there had been a law that could have given life, then 

verily righteousness should have come by the law, 
But righteousness did not come by the law." 
■\ Gal. iii. 21. 

• The fallacy here is that the Disjunction is incomplete. There 
\s another horn, viz : that Protagoras had no cause of action, be- 
cause before the bringing of this suit, Euathlus had no case in 

court. See Chap. VI., 28. 
20 



230 APPENDIX. 

40. Poets are men, 
Orators are men. 



41. Plants are bodies with life, and without consciousness, 
Geraniums are such bodies, 

42. All trees bearing acorns are oaks, 
Some trees do not bear acorns. 

43. All men are rational animals, 
Apes are not men, 

.*. They are not rational animals. 

44. Some men are orators, 
Some bipeds are (all) men, 

,\ Some bipeds are orators. 

45. The following answer was given to Pyrrhus' assertion 
that nothing can be certainly known : 

If you certainly know this, your assertion is disproved, 
If you do not certainly know it, you have no right to 

affirm it, 
But you either do or do not know it, 
Therefore your doctrine is untenable. 

46. Most people are careless, 

Most people are destitute of perfect health. 

47. It is almost certain that C. D. is a true witness because 
there is a probability amounting to § that he saw and ob- 



EXAMPLES FOR PRAXIS. 231 

served correctly what he testifies about, and another proba- 
bility of f that he would tell the truth if he did know it. 

4S What is the probability that B. B. wrote a certain anony- 
fcaous letter, where the separate probabilities are — 
From chirography, J, 
From the sentiments, }, and 
From his known meanness of character, \ ? 

49. All plants contain cellular tissue, 
No animals are plants, 

/. No animals have cellular tissue. 

50. A fungus is a plant, for it is either a plant or an animal, 
and it is not an animal. 

51. If this man were wise, he would not speak irreverently 
of Scripture in jest ; and if he were good, he would not do so 
in earnest ; but he does it, either in jest or earnest ; 



52. Magnets attract iron, and they have polarity, 

53. Insects are not winged, because birds are winged, and 
insects are not birds. 

54. Insects are not fishes, because fish live in water, and in- 
sects do not. 

55. What is the probability of a recurrence next year of a 
fire in one of our great cities, consuming millions of property, 
from the fact that such fires have occurred on an average once 
a year for the last ten years? 



232 APPENDIX. 

56. All these students form a powerful body, 
A. B. is one of these students, 

He forms a powerful body. 

57. What inferences by opposition can be obtained from — 

All men are fallen, 

Some trees are oaks, 

Some stones are not diamonds, 

All triangles are three-sided figures ? 

58. Convert logically — 

Some men are not cultivated. 
Some men are cultivated. 
All plants are living things. 
All pure men love God. 

59. What do you say of dividing college studies into chem 
ical, classical, rhetorical, theoretical, practical, those taught by 
text-book, and those taught by lecture, as a sample of Logical 
Division ? 

60. What do you say of defining a square as a rectangular 
parallelogram, a quadruped as a dog, a triangle as a three- 
sided figure whose angles are equal to two right angles? 

61. Point out the subject, predicate, copula, quantity, and 
quality of the following judgment: 

All students decline in scholarship who become indolent 

62. Body is space-filling substance, 
Body has mobility, 

,\ Whatever has mobility is space-filling. 



EXAMPLES FOR PRAXIS. 233 

63. Discontented persons are not wise, 
Abstemious persons are wise, 

.*. Discontented persons are not abstemious. 

64. Whatever promotes the public good should receive the 
attention of government, 

Dram-shops do not promote the public good, 
,\ They should not receive the attention of government. 

6o. Animals are sensitive beings, 
Sensitive beings have life, 
Beings having life are organized, 
/. Animals are organized. 

66. Useful pursuits ought to be encouraged ; 

Farming, since it produces food for man and beast, is such ; 
.\ It ought to be encouraged, and consequently what de- 
presses it ought to be opposed. 

67. If the earth does not revolve on its axis, existing phe- 
nomena cannot be accounted for; 

It does so revolve, 



68. Silver is money, 
Gold is money, 



69. Perseverance enables us to conquer, 
Therefore it is useful. 

70, All gold is precious, 
This mineral is precious, 

20* 



234 APPENDIX. 

71. Warm countries alone produce oranges, 
Florida is a warm country, 

•\ Florida produces oranges. 

72. The earth moves either in a circle, ellipse, or straight line, 
It does not move in a straight line, 



73. If the atheists are right the world exists without a cause, 
But the atheists are not right, 



74. A religion attended by miracles is from God, for none 
but God can work miracles, and he would not work them in 
behalf of an impostor ; 

The Christian religion was attested by miracles, for in- 
dubitable evidence proves it; 

.". The Christian religion is from God. 

75. Point out the subject, predicate, copula, and distributed 
terms in the following judgments : 

He that believeth hath eternal life. 
Civil office is either legislative, executive, or judicial. 
Circles are figures equidistant at every point from a point 
within. 

/ 6. What can you infer by Opposition and Conversion from — 
All men are liable to become gray, 
Some stars are (all the) planets, 
Some persons are not cheerful ? 

77. Although animals feel, perceive, remember, and have 
instinct like men, they do not know axioms above sense, nor 
have articulate speech, nor increase their knowledge from gen- 



EXAMPLES FOR PRAXIS. 235 

eration to generation, which are higher gifts than the former. 
Men do this, and therefore have more than brute intelligence. 

78. All plants have life, 

But none have consciousness, 



79. If I am to succeed in life, no conduct of mine will pre- 
vent it ; 

If I am to fail, no conduct of mine will prevent it ; 
But one or the other of these is true ; 
.". All effort on my part is useless. 

80. The predictions of weather from Washington having been 
true four days out of five, and it being proposed to increase their 
accuracy — one- tenth by better instruments, one-tenth by increased 
skill in the observers, and one-tenth by the increase of stations 
of observation — what measure of probability may we expect in 
the predictions of next year ? 

81. Many defalcations and breaches of trust have recently 
been discovered, and therefore nobody is worthy of confidence. 

82. What can you infer by all modes of Logical Inference, 
mediate and immediate, from the following judgments, taken 
singly or in any mode of combination ? State and analyze also 
the kind of reasoning, or of syllogism, employed in each in- 
stance : 

A., B., and C. are scholars, 

All scholars are studious, 

All studious persons are diligent. 

83. 1. The following definitions of Logic have been given. Test 
each of them by the proper logical canon for good definition : 



236 APPENDIX. 

a. Logic is the science of reasoning. 

b. Logic is the art of reasoning. 

c. Logic is the science of thought. 

d. Logic is the science of discursive thought. 

e. Logic is the science of the laws of discursive thought, 
/. Logic is the art of improving the mind. 

2. Give a logical division of conceptions according to 
their quality, as clear, distinct, etc. (See Chap. II., 9.) 

3. What can you conclude by any form of inference, 
mediate or immediate, from — 

Men are capable of religion, 
Apes are not capable of religion ? 

84. " The gospel which was preached by me is not after man, 
for I neither received it, neither was I taught it [by man] ; but 
by revelation of Jesus Christ." Gal. i. 11, 12. 

85. " I do not seek to please men, for if I did, I should not 
be the servant of Christ [as I am]." Gal. i. 10. 

86. " But that no man is justified by the law in the sight of 
God is evident : for, the just shall live by faith, and the law is 
not of faith." Gal. iii. 11, 12. 

87. The government cannot outlive the prevalence of Chris- 
tianity among the people, because it is a republic, and republics 
are governed by the people, and only virtuous people are fit to 
govern ; but all experience proves that a people will not remain 
virtuous after it has rejected Christianity. 

88. Paganism, Mohammedanism, Judaism are false ; 
These (according to infidels) are representative of all 

religions ; 



EXAMPLES FOR PRAXIS. 3 3 

89. Reason, conscience, and free-will are requisite to accc x«Ji 
ability, because all possessing them, whether angels or nier, **^ 
accountable ; while those destitute of either of them, as m[<s^% 
idiots, and maniacs, are not accountable. 

90. What can you infer from each of the following judgme<s, 
singly, or from any combination of some or all of them ? — 

All men are rational creatures, 
Rational creatures are progressive, 
Brutes are not progressive. 

91. The ice-crop has failed in a certain region three timer* mi 
twenty years. Compute the probability of its not failing **e 
present winter. 

92. Analyze the two following, and point out their difle) it 
logical force, with reasons : 

1. Parallelograms are plane figures, 
Circles are not parallelograms, 



2. Parallelograms are four- sided plane figures whose oppo? « 
sides are parallel, 

Circles are not parallelograms, 



93. Men are bipeds, so also are birds, and therefore birds t i 
men. 

94. Men of genius are eminent poets, and 
Men of genius are eminent philosophers, 



238 APPENDIX. 

95, All adequate cognitions are distinct, 
All distinct cognitions are clear, 
No clear cognitions are obscure. 

What can you infer from each of the foregoing?— 

1. By Opposition ; 

2. By Conversion, 

3. By the combination of any two of them ; 

4. By the combination of all of them. 

96. The cases of bad drainage known are cases attended with 
Hxdch sickness, 

These cases are (as good as) all cases of it, 



97. Bad weather is followed by good weather, and good 
tveaiher by bad weather, 

•\ The one is the cause of the other. 

98. Supposing the prospects of the completion of a proposed 
building in six months to be nine-tenths from the known prompt- 
itude of the architect and builder, three-fourths from the possi- 
bilities of rapid work in winter, and three-fourths from various 
other contingencies, what is the total chance? 

99. If it is our destiny to be saved, we shall be saved what- 
ever we do or omit to do ; and if we are to be lost, we shall be, 
whatever we may do about it. But we are destined to be saved 
or lost ; whatever we do, therefore, will not affect our destiny, 

100. Moisture is a chief cause of animal putrefaction, because — 

a. It is present where such putrefaction occurs. 

b. Putrefaction is arrested in a perfectly dry atmosphere. 



EXAMPLES FOR PRAXIS. 239 

c. Any variations from this are accounted for by the action 
of other agents. 

101. What do you say of the following as specimens of 
Definition ? — 

a. The United States are composed of the territory and its 
inhabitants, whose central government has its seat at Washington. 

b. The United States are composed of the New England, 
Middle, Southern, South-western, North-western, and Pacific 
States. 

102. Give your opinion of the following definitions and 
divisions of, or under, Applied Logic: 

a. A Fallacy is an unsound mode of reasoning. Logical 
Method is the true mode of reasoning. 

b. Fallacies are divisible into Formal and Material, illicit 
process, argumentum ad verecundiam, and post hoc ergo propter hoc. 

103. What can you infer from the first of the following judg- 
ments by Conversion ; from the second by Equipollence or In- 
finitation ; from the third by Opposition ; from any combination 
of them by Mediate Inference ? — 

The precious metals are gold and silver 
Gold and silver are fusible, 
Fusible metals are evenly divisible. 

104. What can you infer by any mode of Mediate or Im- 
mediate Inference from the following judgments, whether taken 
6ingly or in any possible combination of some or all of them ? — 

Some animals are birds, 

All birds are winged creatures, 

No winged creatures are reptiles. 



k* APPENDIX. 

105. The Bible is a revelation from God if it is attested bj 
idequate miracles, 

It is a revelation from God, 



106. Having for a major premise, 

" Money is either gold, silver, nickel, copper, or paper, 
what can you infer from it with either of the following as a 
minor premise : 

a. This money is gold. 

b. This money is not copper. 

107. If wars enrich many people, they promote the public 
welfare ; 

If they impoverish many people, they are hostile to the 
public welfare ; 

But they both enrich many people and impoverish many 
people, 



108. Very lavish expenditures in railway construction in this 
country preceded, and therefore caused, the financial crisis of 
1873. 

109. The Middle States include a large territory, 
New Jersey is a Middle State, 



110. Inductive reasoning is that which proceeds from par- 
ticular cases to general laws, and is eminently instrumental in 
til® discovery of truth. 



EXAMPLES FOR PRAXIS. 241 

The argument that because A., B., and C. achieved eminence 
without a college education, and therefore a college education 
does not help in attaining eminence, is a case of reasoning from 
particular facts to a general law, and is therefore inductive, and 
hence conclusive. 

Point out any fallacies you discover in the foregoing argu- 
ment, whether in respect to the laws of Formal or of Applied 
Logic, especially in reference to the criteria of a valid inductive 
conclusion. 

111. No one is free who is enslaved by his appetites, 
Every sensualist is so enslaved, 

112. David slew Goliath, 

David was the sweet Psalmist of Israel, 



113. Every liar is vile, 

A vile person should be contemned, 



114. Keligion is the greatest blessing to man, 
Mohammedanism is religion, 



115. It will be clear weather if the clouds rise from the hill 
tops, 

The weather will not be clear, 

116. Barns are structures for the accommodation of animals' 
Barns are not bird-cages, 



21 



242 APPENDIX. 

117. In Opposition, prove the relation of the sub-contraries 
from that of the contradictories. 

118. What can you get by opposition from "Benevolent 
actions are commendable " ? By conversion from " Commend- 
able actions are right " ? By conversion from " Bight actions 
ought to be performed"? By any mode of mediate inference 
from any combination of any two or more of the foregoing 
judgments? In every case of such combination name the 
kind of Syllogism resulting, and analyze it according to the 
laws of that kind. 

119. Free-will, reason, and conscience are requisite to and 
constitute accountability. For wherever they are accountability 
is ; where they are wanting there is no accountability ; and as 
they increase in strength accountability increases. 

120. Men are sensitive and rational, 

/. Brutes, being sensitive, are rational. 

121. Within the last fifteen years the gold dollar has been 
worth two and a half times a legal-tender irredeemable paper 
dollar. It is now equal to such paper dollar. 

.'. Gold is extremely fluctuating in value, and so unfit to 
be used as a measure of value. 

122. Define Science, also Philosophy, and show how they 
differ from each other and from other kinds of knowledge, 

123. Kose-water is a decoction of roses, 
Kose- water is a sweet perfume, 



EXAMPLES FOR PRAXIS. 243 

Besides resolving the foregoing as a Syllogism, show which 
judgment is analytic and which synthetic, and why ; also, whether 
rose-water represents a notative or symbolical conception, and 
why. 

124. What can you infer from " Man is rational," by Oppo- 
sition ? " Man is accountable," by Conversion ? " Man is im- 
mortal," "by ^Reciprocal change of positive and privative con- 
ceptions ? 

Also from the combination of all or any two of these judg- 
ments by any form of inference, mediate or immediate ? 

125. Meat and drink are necessaries of life, 

Meat and drink are what drunkards and gluttons spend 
their substance upon, 



126. Logic is worthy to be cultivated if Aristotle is infallible, 
But he is not, 



127. A. B. is a successful demagogue, 

A successful demagogue must know how to hoodwink 
the people, 

He who knows this must understand their weaknesses, 
He who understands these must lose his respect for them, 



128. All the fish taken in the net were an indiscriminate 
mixture of various kinds, 

Salmon and mackerel were fish that the net enclosed, 



244 APPENDIX. 

129. Nothing is heavier than platinum, 
Feathers are heavier than nothing, 

•\ Feathers are heavier than platinum. 

130. If it is certain that students will be diligent, academic 
honors are useless ; 

And if it is certain they will be idle, such incitementa 
are useless ; 

But one or the other of these is true ; 
.". Academic honors are useless. 

131. Compute the entire probability that the gentleman who 
died with an insurance on his life amounting to a quarter of a 
million of dollars, procured within the previous three months, 
intentionally sought his own death in order to leave this amount 
to his family, the probabilities of this hypothesis being — 

(1) From the enormous amount insured \ 

(2) From the insurance being effected within three months 

of his death \ 

(3) From his imprudent exposure of himself to attacks 

of disease \ 

(4) From his previously having lost his wife's large 

patrimony in speculation.... \ 

The counter-probabilities being — 

(1) From his unblemished character \ 

(2) And from his having carried very heavy life insur- 

ance at former periods of his life } 

132. Find the genus and differentia, if there be any, and giva 
the logical character of the following definitions : 



EXAMPLES FOR PRAXIS. 245 

Dew is a natural deposit of water on the earth which is 
neither rain nor fog. 

Logic is a mental science. 

Conversion of Judgments is making the subject and predicate 
change places. 

A category is a predicable. Also, 

Define Logic by the method of Resolution, also of Colligation. 

133. Give a Logical Division of Applied Logic, descending 
through the divisions and subdivisions of Fallacies. Also of 
Kant's categories. 

134. What Inference free from all Fallacy can you get— a, by 
Opposition ; b, by Conversion ; c, by Mediate Inference — from 

All civilized persons are educated, and 
None but civilized persons are Christians, 
.• ? 

135. The tastes of men are variable, but what is according to 
the constitution of nature is invariable, 



136. Reasoning by Analogy is inconclusive, 
Butler's Analogy is such reasoning, 



137. Cloven feet being found universally in horned animals, 
we may conclude that this fossil animal was horned, since its 
feet are cloven. 

138. Hypotheses have often proved a fruitful means of dis- 

21* 



246 APPENDIX. 

covering and testing truth, and therefore they ought to be 
accepted. 

239. Taking the definition of Dew above given, analyze logi- 
cally the following argument, to prove that it results from the 
condensation of moisture in the air by contact with the earth 
when colder than such air: 

1. This is the universal law of such contact of warm air upon 
colder surfaces, as is proved — 

x. From the water formed on the outside of ice-pitchers, 
y. Also on the surface of stones colder than the air, 

2. On walls of unfurred rooms, 

to. From water or ice formed on the inside of window-glass 
suddenly chilled. 

Again, no water is deposited on surfaces as warm as the air 
in contact with them, as appears — 

x. From pitchers or crockery as warm as the surrounding 
air, 

y. Panes of glass when it is warm outside, 

2. Stones warmed by the sun. 

II. The earth at night in a clear atmosphere, such as that in 
which dew is formed, is made cooler than the air in contact with 
it by the radiation of its heat through the atmosphere in all ob- 
served instances — x, y } z, w. 

Again, no dew is formed in case of the earth being as warm 
as the air, as is shown — 

x. In cloudy nights, 

y. At mid-day, 

g. In decidedly cold weather. 

Still further, the amount of dew formed varies with the 



EXAMPLES FOR PRAXIS. 247 

amount of moisture in the atmosphere and the extent to which 
it is warmer than the earth, as appears, because — 

x. When the air becomes suddenly hot and surcharged with 
moisture the dews are heaviest, 
y. There is little dew in time of drouth, 
s. There is average dew in average clear weather. 



APPENDIX B. 

SYLLOGISTIC NOT AT 10 IT. 

1 Various methods have been adopted to represent to 
the eye the different forms of the Syllogism, 

Meaning of ' Syl- and the re i at i ons f thought respectively in- 
logistio Nota- 
tion, volved in them. This is done through linear 

diagrams analogous to the figures of Geom- 
etry. It greatly assists the mind in discerning at a glance 
the quantity, the mutual relation, and the quality of the 
different terms and judgments of the syllogism, together 
with its figure and mood. One of the most celebrated 
schemes of notative symbols is that by means of circles in- 
vented by Euler, upon which we have already 
Enler's Method , n , .,, 

bv Circles drawn tor purposes 01 casual illustration. 

(See Chap. V. 13.) 

2. Three circles are employed to denote respectively the 
Major, Minor and Middle Terms. Affirmative judgments are 
symbolized by the total or partial inclusion of the circle signi- 
fying the subject in that which stands for the predicate. 

Negatives are signified by the total or partial exclusion 
of the former from the latter. 

The following diagram, in which A B and C denote re 
gpectively the minor, middle, and major terms, represents, 

248 



SYLL GISTIC NO TA TION. 



249 



1. The moods A A A. 2. AEE. 3. A I L 4. EI 0, all 

of the First Figure. 



1. Barbara. 




2. Celarent 




3. Darii. 




4. Ferio. 




Of course, this method, mutatis mutandis^ is applicable to 

the other figures. This clearly and beautifully represents the 

Syllogism according to extension, as also the distribution 

or non-distribution of different terms. 
20* 



250 APPENDIX. 



NOTATION BY STRAIGHT LINES. 

4. According to this scheme, a horizontal straight line 
denotes a term distributed. The letters S, P, or M attached, 
indicate that it is respectively minor, major, or middle term. 

S 

P 

Dots are used to signify an undistributed term as noting 
its indefiniteness. 



M 



Any definite portion of an undistributed term is indicated 
by a line not dotted inserted in one that is dotted. Thus in 
the judgment "men are mortal,' ' i. e. "some mortals,' ' 
mortal is undistributed. But we take that definite portion 
of it which is co-extensive with the class man. Thus : 



mortal. 



S men. 

Affirmative judgments are symbolized bylines, one above 
the other — the former being the predicate, the latter the 
subject. Negative judgments are represented by parallel 
lines drawn so that one is not under the other. Thus : 



To complete the syllogism, of course three lines must be 
employed to represent the three terms and judgments iu 
their quantity and other relations. 



SYLLOGISTIC NOTA TION. 25 i 

P 



•••••«•«• 



M 

S. 



This represents A A A, of Fig. 1. Thus : 

All horses are quadrupeds, 
All Shetland ponies are horses, 
•\ All Shetland ponies are quadrupeds. 

If there be one negative premise in the Syllogism, it can 
be thus represented. The following is E A E, Celarent, 
of Fig. 1. 

P 

M 

S 



No M is P, 

All S is M, 
/. No S is M. 

Substitutive Judgments are indicated by two equal and 
parallel lines. Thus : 

P 

S 



J udgments of Logical Division or Colligation (chap. II. 43) 
may be expressed thus : 

_. . . P x y z P 

Division, ^ Colligation, „ 

S S — x — y — I 



252 APPENDIX. 

THE HAMILTONIAN NOTATION. 

5. Quite the most expressive and complete system of 
Notation, and one of his important contributions to Logic, 
is that invented by Sir William Hamilton. It is so con- 
trived as to exhibit, at a glance, all the characteristics of 
the valid Syllogism, both according to intension and exten- 
sion, in all the figures. This is done by means of lines, 
wedge-shaped in the figured Syllogism, and of uniform length 
and breadth in the unfigured Syllogism, and in all substitu- 
tive judgments, these latter lines denoting the perfect 
equality of subject and predicate. 

6. The wedge-shaped figure or line denotes a judgment- 
its thick end the subject of extension which is contained 
extensively in the predicate : its thin end the subject of in- 
tension, or predicate of extension, which is contained inten 
sively in the other. Most of what follows is so well put in 
Bowen's Logic, that we transfer it with little modification. 

" As the employment of letters following upon each other 
in the same alphabet might suggest that one was invariably 
subordinated to the other, instead of being its subordinate 
in one Quantity and its superordinate in the other, Hamil- 
ton uses for the Extremes the Latin C and Greek r, each 
being the third letter in its own alphabet; as usual, M 
stands for Middle Term. Thus : 

is read, C and r are equal. 

may be read in two ways; Extensively, C is included undei 



SFLL GISTIC NOT A TION. 253 

I ; Intensively, r is included in C: — or, in the usual manner, 
C is r, and r is (7, merely remembering, without saying so, 
that Extension is signified in the former case, and Inten- 
sion in the latter. 

7. "Negation is indicated by a perpendicular stroke 
drawn through the line, thus : ■ 1 . The line without 
this stroke may be regarded as the Affirmative Copula ; with 
the stroke, as the Negative Copula. A colon ( : ) annexed 
to a Term shows that it is distributed, or taken universally ; 
a comma ( , ) so annexed, that it is undistributed or Parti- 
cular. When a Middle Term has a colon on the right, and 
a comma on the left, it is understood that it is distributed 
when coupled in a Judgment with the Term on the right, 
and undistributed when coupled with the other. 

8. " A line drawn beneath or above three Terms indicates 
the Conclusion (or the Copula of the Conclusion) deduced 
from the two Premises which those Terms constitute. In 
the Second and Third Figures, since there may be two 
equally direct or immediate Conclusions, they are represented 
by two such lines, the one above, and the other below the 
Premises. Thus : 

n ^— M — T r Thi s is a Syllogism in the Second 

* ' — — ' Figure, which may be read in either 

of the following ways. 

Extensively. Intensively. 

Some C is some M ; All M is some r; 

Some r is all M ; Some M is some C; 

.*, Some r is some C; or .'. Some C is some r; or 

,% Some C is some r. .". Some r is some C. 

22 



254 APPENDIX. 

C, ■, M: — 4— «: r "This is a negative Syllogism 
] — — in the First Figure, which may be 
read in. either of the following ways; but in either way, it 
has only one direct or immediate Conclusion, though a 
Seoond Conclusion may be obtained from it ttw&toig/, by 
converting simply the propei or direct Conclusion. 

Extensively. Intensively, 

Some M is some C; No M is any r; 

No r is any M; Some C is some M; 

No r is some C; or, Some C is not any r; or % 

indirectly. indirectly. 

Some C is not any r ; Not any r is some C. 

9. "The following diagram presents the whole Hamil- 
tonian doctrine of Figure, together with the distinction 
between the Analytic and the Synthetic order of enounce- 
ment. After the explanations which have been given, it will 
be easily understood. 

" As a Judgment has been designated by a line, a Syllo- 
gism, which is a union of three Judgments, is appropriately 
typified by a triangle, a union of three lines, of which the 
base represents the Conclusion, and the other two lines, the 
Premises. As the direction of the arrows indicates, we may 
proceed either in the usual or Synthetic order, from the 
Premises to the Conclusion, or in the reverse order, which 
is Analytic, from the Conclusion to the Premises. As there 
is no valid reason for always placing the Major Premise 
first in order, the diagram shows that either Premise may 
have precedence in this respect, so that what has been 



SYLLOGISTIC NOTATION. 



255 



sailed the Fourth Figure is here identified with the Indirect 
Moods of the First 




X X X 



41 The Unfigured Syllogism is properly represented as in- 
cluding all the others, as any Syllogism of either Figure may 
be easily expressed in this form. In like manner th8 
triangle representing the First Figure is made to include the 
two typifying respectively the Second and Third, as either 
of the latter may be readily reduced to the former. And 
again, the essential unity of the Syllogistic process, and the 
unessential nature of variation by Figure, are appropriately 
signified by a single triangle comprehending all the varietiei 
of form. 



256 APPENDIX. 

"The double Conclusions, both equally direct, in the 
Second and Third Figures, are shown in the crossing of two 
counter and corresponding lines. The Direct and Indirect 
Conclusions in the First Figure are distinctly typified by a 
common and by a broken line; the broken line is placed 
immediately under the other, and may thus indicate that it 
represents only a reflex of — a consequence through the 
other." 

10. It will be remembered that the four fundamental 
judgments hitherto recognized by logicians, viz. , A E I 0, 
yield sixty-four conceivable moods. Excluding from these all 
that are invalid as offending against the laws of the syllogism, 
only eleven moods remain that are valid in the fourteen syl- 
logisms of the first three figures, or nineteen, if the fourth 
figure be recognized. But Hamilton, as we have seen, recog- 
nizes eight judgments, adding to the four already named, U 
Yiw. The possible combinations of these are five hundred 
and twelve. Of this number, however, only thirty-six will 
bear the tests of valid syllogisms, of which twelve are aflirma- 
mative and twenty-four negative. Thus, on this system, 
each affirmative mood has two corresponding ones that are 
negative, as each of its premises may be made negative. 
Since each of the moods on this system can be put in 
either of the three figures, there arise three times thirty- 
six, or one hundred and eight valid syllogisms in the several 
figures. The changes in the different figures, however, aro 
for the most part unessential and insignificant. The follow- 
ing table by Hamilton exhibits the eight judgments re- 
cognized by him, very ingeniously in their relative strength. 



SYLLOGISTIC NOTATION. 



257 



in which A signifies a term distributed, I a term undistri* 
buted, f an Affirmative, and n a Negative copula. A par- 
ticular is accounted weaker than a universal, and a negative 
weaker than an affirmative. 



Best. 



Worst. 



L 



-1. Afa. All are all. 

-2. Afi. All are some. 

-3. Ifa. Some are all. 

Ifi. Some are some. 

5. Ini. Some are not some. 

-6. Ina. Some are not any. 

-7. Ani. Not any is some. 

-8. Ana. Not any is any. 



11 With these explanations, the following list of the twelve 
valid Affirmative Moods in each of the three Figures, and 
the twenty-four valid Negative Moods in the First Figure, 
all expressed in the Hamiltonian notation, will be found 
intelligible. 

11. "In this Table, the Quantity of the Conclusion is 
marked only in the cases already considered, wherein the 
Terms obtain a different Quantity from that which they 
held in the Premises ; accordingly, when not marked, the 
quantification of the Premises is held as repeated in the 
Conclusion. The symbol v -^-', placed beneath a Conclusion, 
indicates that, when the Premises are converted, the Syllo- 
gism remains in the same Mood ; ^><C shows that the two 
Moods between which it stands are convertible into each 

other by converting their Premises. The Middle Term is 
22* R 



258 



APPENDIX. 



THE HAMILTONIAN ANALYSIS AND SCHEME 

TABLE OF SYLLO- 

A. AFFIRMATIVE MOODS. 



B 



i. C- 



ii. C- 



iii. C, 



It. Cr 



v. C, 



vi. C, 



vii. C:- 



viii. C, 



ix. C: 



x. C: 



xi. C:- 



Fig. I. 
■ : M : - 



:M: 



i: M, 



&. 



:M,- 



X 

,M:- 



[ ;M: 



X 

:M: - 



:M, 



X 

i ,M: ■ 



> :M, 



■ :r 0:. 

■:r c,I 

■,r C:« 

■,r Cm 

-,r c,- 



■ f r C: 



■ :T c, 



b: T C :■ 



, r C :■ 



X 

*H- C , ■■« , M : — :T C, 



Fig. ii. 



:M: 



■: r 



: M : ■ 



■, r 



w^ 



:M,. 



■:T 



X 



,M: 



:M, 



■, r 



X 



,M:. 



:M:« 



*, r 



X 



■:M: ■ 



■:M, 



X 



,M:- 



:M, ■ 



X 



,M: 



*.T 



WOfl.— A. 1. and ii. are Balanced. B. The other moods are Unbalanced. Of these, 



SYLLOGISTIC NOTATION. 



259 



OF NOTATION— FIGURED SYLLOGISM. 

GISTIC MOODS. 

A. AFFIRMATIVE MOODS. 

Fig. hi. 

"~":r 




08- 



c,- 



■:M,i 



X 



.,M:. 



-,r 






Hi. and iv. are unbalanced in terms only, n it in propositions ; the rest in both. 



260 APPENDIX. 

said to be balanced, when it is Universal in both Premises. 
The Extremes, or Terms of the Conclusion, are balanced^ 
when both alike are distributed ; unbalanced, when one is, 
and the other is not, distributed. Accordingly, of the 
Moods, in this Table, numbers I. and II. are balanced aa 
respects both terms and propositions; in III. and IV., only 
the terms are unbalanced; in the remainder both terms 
and propositions are unbalanced/ ' 



'CM L 



£ 1 A 1 A 9 4 




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